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Distinguished Professor Robert McLachlan staff profile picture

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Distinguished Professor Robert McLachlan BSc(H), PhD, FRSNZ

Distinguished Professor in Applied Mathematics

Doctoral Supervisor
School of Mathematical and Computational Sciences

Robert McLachlan studied at Canterbury and Caltech and has worked at the University of Colorado at Boulder and ETH Zurich. He has been a research fellow at the Isaac Newton Institute, Cambridge, the Mathematical Sciences Research Institute, Berkeley, and the Center for Advanced Study, Oslo. Since its founding in the early 1990s he has been a leader in the new field of geometric numerical integration, a technique for the reliable simulation of large-scale complex systems, especially those arising in computational physics and chemistry.

Professional

Contact details

  • Ph: 06 951 7652
    Location: ScB3.22, Science Tower B
    Campus: Turitea

Qualifications

  • Bachelor of Science (Hons) - University of Canterbury (1984)
  • Doctor of Philosophy - California Institute of Technology (1990)

Fellowships and Memberships

  • Member, Royal Society of New Zealand (Fellow) (2002)

Research Expertise

Research Interests

Numerical solution of differential equations, especially geometric numerical integration.

Numerical analysis including optimization and image processing.

Thematics

Resource Development and Management

Area of Expertise

Field of research codes
Algebraic Structures in Mathematical Physics (010501): Applied Mathematics (010200): Applied Mathematics not elsewhere classified (010299): Calculus of Variations, Systems Theory and Control Theory (010203): Dynamical Systems in Applications (010204): Integrable Systems (Classical and Quantum) (010502): Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory (010503): Mathematical Physics (010500): Mathematical Sciences (010000): Numerical and Computational Mathematics (010300): Numerical Solution of Differential and Integral Equations (010302): Optimisation (010303): Theoretical and Applied Mechanics (010207)

Keywords

Numerical analysis, scientific computation, simulation, symplectic integrators, image processing.

Research Projects

Completed Projects

Project Title: Geometric numerical integration: new structures and applications

Date Range: 2015 - 2019

Funding Body: Royal Society of New Zealand

Project Team:

Project Title: Geometric Integration

Geometric integration is a novel approach to simulating the motion of large systems. The new methods, inspired by chaos theory but driven by the demands of modern applications are faster, more reliable, and often simpler than traditional approaches. They are being used in areas as diverse as the celestial origin of the ice ages, the structure of liquids, polymers, and biomolecules, quantum mechanics and nanodevices, biological models, chemical reactiondiffusion systems, the dynamics of flexible structures, and weather forecasting. Although diverse, these systems have certain things in common that makes them amenable to the new approach. They all preserve some underlying geometric structure which influences the qualitative nature of the phenomena they produce. In geometric integration these properties are built into the numerical method, which gives the method markedly superior performance, especially during long simulations. In our research we are exploring the geometric or structural features that systems can have, the implications for their long-time dynamics, and how to design efficient numerical integrators that preserve these geometric properties.
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Date Range: 2008 - 2012

Funding Body: Marsden Fund - Full

Project Team:

Research Outputs

Journal

van der Kamp, PH., McLachlan, RI., McLaren, DI., & Quispel, GRW. (2024). MEASURE PRESERVATION AND INTEGRALS FOR LOTKA–VOLTERRA TREE-SYSTEMS AND THEIR KAHAN DISCRETISATION. Journal of Computational Dynamics. 11(4), 468-484
[Journal article]Authored by: McLachlan, R.
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Bogfjellmo, G., Celledoni, E., Mclachlan, RI., Owren, B., & Quispel, GRW. (2024). USING AROMAS TO SEARCH FOR PRESERVED MEASURES AND INTEGRALS IN KAHAN’S METHOD. Mathematics of Computation. 93(348), 1633-1653
[Journal article]Authored by: McLachlan, R.
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Ghosh, I., McLachlan, RI., & Simpson, DJW. (2024). The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps. Communications in Nonlinear Science and Numerical Simulation. 134
[Journal article]Authored by: Ghosh, I., McLachlan, R., Simpson, D.
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Callister, P., & McLachlan, RI. (2024). Managing Aotearoa New Zealand's greenhouse gas emissions from aviation. Journal of the Royal Society of New Zealand. 54(4), 412-432
[Journal article]Authored by: McLachlan, R.
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Laurent, A., Mclachlan, RI., Munthe-Kaas, HZ., & Verdier, O. (2023). The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators. Forum of Mathematics, Sigma. 11
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., McLaren, DI., & Quispel, GRW. (2023). Birational maps from polarization and the preservation of measure and integrals. Journal of Physics A: Mathematical and Theoretical. 56(36)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Offen, C. (2023). Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics. 15(1), 98-115
[Journal article]Authored by: McLachlan, R.
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Muni, SS., McLachlan, RI., & Simpson, DJW. (2022). UNFOLDING GLOBALLY RESONANT HOMOCLINIC TANGENCIES. Discrete and Continuous Dynamical Systems- Series A. 42(8), 4013-4030
[Journal article]Authored by: McLachlan, R., Simpson, D.
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McLachlan, RI., & Stern, A. (2024). Functional Equivariance and Conservation Laws in Numerical Integration. Foundations of Computational Mathematics. 24(1), 149-177
[Journal article]Authored by: McLachlan, R.
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Brown, R., Marsland, S., & McLachlan, R. (2022). Differential Invariant Signatures for Planar Lie Group Transformations with Application to Images. Journal of Lie Theory. 32(3), 709-736
[Journal article]Authored by: Brown, R., McLachlan, R.
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McLachlan, RI., & Offen, C. (2022). BACKWARD ERROR ANALYSIS FOR VARIATIONAL DISCRETISATIONS OF PDES. Journal of Geometric Mechanics. 14(3), 447-471
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (2022). Tuning Symplectic Integrators is Easy and Worthwhile. Communications in Computational Physics. 31(3), 987-996
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., Ehrhardt, MJ., Etmann, C., Mclachlan, RI., Owren, B., Schonlieb, CB., . . . Sherry, F. (2021). Structure-preserving deep learning. European Journal of Applied Mathematics. 32(5), 888-936
[Journal article]Authored by: McLachlan, R.
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Muni, SS., McLachlan, RI., & Simpson, DJW. (2021). Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions. Discrete and Continuous Dynamical Systems- Series A. 41(8), 3629-3650
[Journal article]Authored by: McLachlan, R., Simpson, D.
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Marsland, S., McLachlan, RI., & Zarre, R. (2021). Analysing ‘Simple’ Image Registrations. Journal of Mathematical Imaging and Vision. 63(4), 528-540
[Journal article]Authored by: McLachlan, R.
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Marsland, S., McLachlan, RI., & Tufail, MY. (2020). CONFORMAL IMAGE REGISTRATION BASED on CONSTRAINED OPTIMIZATION. ANZIAM Journal. 62(3), 235-255
[Journal article]Authored by: McLachlan, R.
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Kreusser, LM., Mclachlan, RI., & Offen, C. (2020). Detection of high codimensional bifurcations in variational PDEs. Nonlinearity. 33(5), 2335-2363
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Offen, C. (2020). Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation. Foundations of Computational Mathematics. 20(6), 1363-1400
[Journal article]Authored by: McLachlan, R.
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Marsland, S., McLachlan, RI., & Wilkins, MC. (2020). Parallelization, initialization, and boundary treatments for the diamond scheme. Numerical Algorithms. 84(2), 761-779
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Stern, A. (2020). Multisymplecticity of Hybridizable Discontinuous Galerkin Methods. Foundations of Computational Mathematics. 20(1), 35-69
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., & McLachlan, RI. (2019). Preface special issue in honor of reinout quispel. Journal of Computational Dynamics. 6(2), i-v
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Murua, A. (2019). The lie algebra of classical mechanics. Journal of Computational Dynamics. 6(2), 345-360
[Journal article]Authored by: McLachlan, R.
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Curry, C., Marsland, S., & McLachlan, RI. (2019). Principal symmetric space analysis. Journal of Computational Dynamics. 6(2), 251-276
[Journal article]Authored by: McLachlan, R.
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Benn, J., Marsland, S., McLachlan, RI., Modin, K., & Verdier, O. (2019). Currents and Finite Elements as Tools for Shape Space. Journal of Mathematical Imaging and Vision. 61(8), 1197-1220
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Offen, C., & Tapley, BK. (2019). Symplectic integration of PDEs using clebsch variables. Journal of Computational Dynamics. 6(1), 111-130
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (2019). Perspectives on geometric numerical integration. Journal of the Royal Society of New Zealand. 49(2), 114-125
[Journal article]Authored by: McLachlan, R.
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Van Der Kamp, PH., Celledoni, E., McLachlan, RI., McLaren, DI., Owren, B., & Quispel, GRW. (2019). Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation. Journal of Physics A: Mathematical and Theoretical. 52(4)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Offen, C. (2019). Symplectic integration of boundary value problems. Numerical Algorithms. 81(4), 1219-1233
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Offen, C. (2018). Bifurcation of solutions to Hamiltonian boundary value problems. Nonlinearity. 31(6), 2895-2927
[Journal article]Authored by: McLachlan, R.
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Grimm, V., McLachlan, RI., McLaren, DI., Quispel, GRW., & Schönlieb, CB. (2017). Discrete gradient methods for solving variational image regularisation models. Journal of Physics A: Mathematical and Theoretical. 50(29)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., & Verdier, O. (2017). A minimal-variable symplectic integrator on spheres. Mathematics of Computation. 86(307), 2325-2344 Retrieved from http://www.ams.org/journals/mcom/2017-86-307/S0025-5718-2016-03153-1/home.html
[Journal article]Authored by: McLachlan, R.
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Mclachlan, R., Modin, K., & Verdier, O. (2017). A minimal-variable symplectic integrator on spheres. Mathematics of Computation. 86(307), 2325-2344
[Journal article]Authored by: McLachlan, R.
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Marsland, S., & McLachlan, RI. (2016). Möbius invariants of shapes and images. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 12
[Journal article]Authored by: McLachlan, R.
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Symes, LM., McLachlan, RI., & Blakie, PB. (2016). Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation. Physical Review E. 93(5)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., & Verdier, O. (2016). Symmetry reduction for central force problems. European Journal of Physics. 37(5)
[Journal article]Authored by: McLachlan, R.
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McDonald, F., McLachlan, RI., Moore, BE., & Quispel, GRW. (2016). Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations. Journal of Difference Equations and Applications. 22(7), 913-940
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., & Verdier, O. (2016). Geometry of Discrete-Time Spin Systems. Journal of Nonlinear Science. 26(5), 1507-1523
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., Munthe-Kaas, H., & Verdier, O. (2016). B-series methods are exactly the affine equivariant methods. Numerische Mathematik. 133(3), 599-622
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., McLachlan, RI., McLaren, DI., Owren, B., & Quispel, GRW. (2015). Discretization of polynomial vector fields by polarization. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 471(2184)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., & Verdier, O. (2015). Collective Lie-Poisson integrators on R<sup>3</sup>. IMA Journal of Numerical Analysis. 35(2), 546-560
[Journal article]Authored by: McLachlan, R.
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Mclachlan, RI., & Wilkins, MC. (2015). The multisymplectic diamond scheme. SIAM Journal on Scientific Computing. 37(1), A369-A390
[Journal article]Authored by: McLachlan, R.
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Mclachlan, RI., Ryland, BN., & Sun, Y. (2014). High order multisymplectic Runge-Kutta methods. SIAM Journal on Scientific Computing. 36(5), A2199-A2226
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., I McLachlan, R., I McLaren, D., Owren, B., & Quispel, GRW. (2014). Integrability properties of Kahans method. Journal of Physics A: Mathematical and Theoretical. 47(36)
[Journal article]Authored by: McLachlan, R.
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Marsland, S., McLachlan, RI., Modin, K., & Perlmutter, M. (2014). On conformal variational problems and free boundary continua. Journal of Physics A: Mathematical and Theoretical. (14)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., & Verdier, O. (2014). Symplectic integrators for spin systems. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 89(6)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., & Verdier, O. (2014). Collective symplectic integrators. Nonlinearity. 27(6), 1525-1542
[Journal article]Authored by: McLachlan, R.
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Mclachlan, RI., & Stern, A. (2014). Modified trigonometric integrators. SIAM Journal on Numerical Analysis. 52(3), 1378-1397
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Quispel, GRW. (2014). Discrete gradient methods have an energy conservation law. Discrete and Continuous Dynamical Systems- Series A. 34(3), 1099-1104
[Journal article]Authored by: McLachlan, R.
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I McLachlan, R., Modin, K., Verdier, O., & Wilkins, M. (2014). Geometric Generalisations of shake and rattle. Foundations of Computational Mathematics. 14(2), 339-370
[Journal article]Authored by: McLachlan, R.
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Marsland, S., McLachlan, RI., Modin, K., & Perlmutter, M. (2013). Geodesic warps by conformal mappings. International Journal of Computer Vision. 105(2), 144-154
[Journal article]Authored by: McLachlan, R.
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Marsland, S., McLachlan, RI., Modin, K., & Perlmutter, M. (2013). Geodesic Warps by Conformal Mappings. INTERNATIONAL JOURNAL OF COMPUTER VISION. 105(2), 144-154
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., McLachlan, RI., Owren, B., & Quispel, GRW. (2013). Geometric properties of Kahan's method. Journal of Physics A: Mathematical and Theoretical. 46(2)
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Modin, K., Verdier, O., & Wilkins, M. (2013). Symplectic integrators for index 1 constraints. SIAM Journal on Scientific Computing. 35(5)
[Journal article]Authored by: McLachlan, R.
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Marsland, S., McLachlan, RI., Modin, K., & Perlmutter, M. (2012). Geodesic Warps by Conformal Mappings. International Journal of Computer Vision. , 1-11
[Journal article]Authored by: McLachlan, R.
Celledoni, E., Grimm, V., McLachlan, RI., McLaren, DI., O'Neale, D., Owren, B., . . . Quispel, GRW. (2012). Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method. Journal of Computational Physics. 231(20), 6770-6789
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Zhang, X. (2011). Asymptotic blowup profiles for modified Camassa-Holm equations. SIAM Journal on Applied Dynamical Systems. 10(2), 452-468
[Journal article]Authored by: McLachlan, R.
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Mclachlan, RI., Sun, Y., & Tse, PSP. (2011). Linear stability of partitioned runge-kutta methods. SIAM Journal on Numerical Analysis. 49(1), 232-263
[Journal article]Authored by: McLachlan, R.
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Modin, K., Perlmutter, M., Marsland, S., & McLachlan, R. (2011). On Euler-Arnold equations and totally geodesic subgroups. Journal of Geometry and Physics. 61(8), 1446-1461
[Journal article]Authored by: McLachlan, R.
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Elvin, AJ., Laing, CR., McLachlan, RI., & Roberts, MG. (2010). Exploiting the Hamiltonian structure of a neural field model. Physica D: Nonlinear Phenomena. 239(9), 537-546
[Journal article]Authored by: Laing, C., McLachlan, R.
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McLachlan, RI., & O'Neale, DRJ. (2010). Preservation and destruction of periodic orbits by symplectic integrators. Numerical Algorithms. 53(2-3), 343-362
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., McLachlan, RI., Owren, B., & Quispel, GRW. (2010). On conjugate B-series and their geometric structure. Journal of Numerical Analysis, Industrial and Applied Mathematics. 5(1-2), 85-94
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., McLachlan, RI., Owren, B., & Quispel, GRW. (2010). Energy-Preserving Integrators and the Structure of B-series. Foundations of Computational Mathematics. 10(6), 673-693
[Journal article]Authored by: McLachlan, R.
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Oneale, DRJ., & McLachlan, RI. (2009). Reconsidering trigonometric integrators. ANZIAM Journal. 50(3), 320-332
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Quispel, GRW., & Tse, PSP. (2009). Linearization-preserving self-adjoint and symplectic integrators. BIT Numerical Mathematics. 49(1), 177-197
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (2009). The structure of a set of vector fields on poisson manifolds. Journal of Physics A: Mathematical and Theoretical. 42(14)
[Journal article]Authored by: McLachlan, R.
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McLachlan, R., & Zhang, X. (2009). Well-posedness of modified Camassa-Holm equations. Journal of Differential Equations. 246(8), 3241-3259
[Journal article]Authored by: McLachlan, R.
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Hairer, E., McLachlan, RI., & Skeel, RD. (2009). On energy conservation of the simplified takahashi-imada method. Mathematical Modelling and Numerical Analysis. 43(4), 631-644
[Journal article]Authored by: McLachlan, R.
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Celledoni, E., McLachlan, RI., McLaren, DI., Owren, B., Quispel, GRW., & Wright, WM. (2009). Energy-preserving runge-kutta methods. ESAIM: Mathematical Modelling and Numerical Analysis. 43(4), 645-649
[Journal article]Authored by: McLachlan, R.
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McLachlan, R., Munthe-Kaas, H., Quispel, R., & Zanna, A. (2008). Foundations of Computational Mathematics: Guest Editors' Preface. Foundations of Computational Mathematics. 8(3), 289-290
[Journal article]Authored by: McLachlan, R.
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Hairer, E., McLachlan, RI., & Razakarivony, A. (2008). Achieving Brouwer's law with implicit Runge-Kutta methods. BIT Numerical Mathematics. 48(2), 231-243
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Munthe-Kaas, HZ., Quispel, GRW., & Zanna, A. (2008). Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. Foundations of Computational Mathematics. 8(3), 335-355
[Journal article]Authored by: McLachlan, R.
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Ryland, BN., & Mclachlan, RI. (2007). On multisymplecticity of partitioned Runge-Kutta methods. SIAM Journal on Scientific Computing. 30(3), 1318-1340
[Journal article]Authored by: McLachlan, R.
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Ryland, BN., Mclachlan, RI., & Frank, J. (2007). On the multisymplecticity of partitioned Runge-Kutta and splitting methods. International Journal of Computer Mathematics. 84(6), 847-869
[Journal article]Authored by: McLachlan, R.
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Mclachlan, RI. (2007). A new implementation of symplectic Runge-Kutta methods. SIAM Journal on Scientific Computing. 29(4), 1637-1649
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Marsland, S. (2007). N-particle dynamics of the Euler equations for planar diffeomorphisms. Dynamical Systems. 22(3), 269-290
[Journal article]Authored by: McLachlan, R.
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Quispel, R., & McLachlan, R. (2006). Preface: Geometric numerical integration of differential equations. Journal of Physics A: Mathematical and General. 39(19), 1
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Quispel, GRW. (2006). Geometric integrators for ODEs. Journal of Physics A: Mathematical and General. 39(19), 5251-5285
[Journal article]Authored by: McLachlan, R.
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Mason, IG., McLachlan, RI., & Gerard, DT. (2006). A double exponential model for biochemical oxygen demand. Bioresource Technology. 97(2), 273-282
[Journal article]Authored by: McLachlan, R.
McLachlan, RI., & O'Neale, DRJ. (2006). Geometric integration for a two-spin system. Journal of Physics A: Mathematical and General. 39(27)
[Journal article]Authored by: McLachlan, R.
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McLachlan, R., & Perlmutter, M. (2006). Integrators for nonholonomic mechanical systems. Journal of Nonlinear Science. 16(4), 283-328
[Journal article]Authored by: McLachlan, R.
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Quispel, GR., & McLachlan, RI. (2006). Geometric numerical integration of differential equations. Journal of Physics A: Mathematical and General. 39(19), 1-3
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Marsland, SR. (2006). The Kelvin–Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms. SIAM Journal on Applied Dynamical Systems. 5(4), 726-758
[Journal article]Authored by: McLachlan, R.
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Ascher, UM., & McLachlan, RI. (2005). On symplectic and multisymplectic schemes for the KdV equation. Journal of Scientific Computing. 25(1-2), 83-104
[Journal article]Authored by: McLachlan, R.
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Mason, IG., McLachlan, RI., & Gérard, DT. (2006). A double exponential model for biochemical oxygen demand. Bioresource Technology. 97(2), 273-282
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Zanna, A. (2005). The discrete Moser-Veselov algorithm for the free rigid body, revisited. Foundations of Computational Mathematics. 5(1), 87-123
[Journal article]Authored by: McLachlan, R.
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Ascher, UM., & Mclachlan, RI. (2005). On symplectic and multisymplectic schemes for the KdV equation. Journal of Scientific Computing. 25(1), 83-104
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Quispel, GRW. (2004). Explicit geometric integration of polynomial vector fields. BIT Numerical Mathematics. 44(3), 515-538
[Journal article]Authored by: McLachlan, R.
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Ascher, UM., & McLachlan, RI. (2004). Multisymplectic box schemes and the Korteweg-de Vries equation. Applied Numerical Mathematics. 48(3-4), 255-269
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Perlmutter, MJ. (2004). Energy drift in reversible time integration. Journal of Physics A: Mathematical and General. 37, L593-L598
[Journal article]Authored by: McLachlan, R.
Kathirgamanathan, P., McKibbin, R., & McLachlan, RI. (2004). Source release-rate estimation of atmospheric pollution from a non-steady point source at a known location. Environmental Modeling and Assessment. 9(1), 33-42
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (2004). [Untitled]. Newsletter of the New Zealand Mathematical Society. 90, 49-50
[Journal article]Authored by: McLachlan, R.
McLachlan, RI., Perlmutter, M., & Quispel, GRW. (2004). On the nonlinear stability of symplectic integrators. BIT Numerical Mathematics. 44(1), 99-117
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Perlmutter, M. (2004). Energy drift in reversible time integration. Journal of Physics A: Mathematical and General. 37(45)
[Journal article]Authored by: McLachlan, R.
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Rynhart, PR., McLachlan, RI., Jones, JR., & McKibbin, R. (2003). Solution of the Young-Laplace equation for three particles. Research Letters in the Information and Mathematical Sciences. 5, 119-127
[Journal article]Authored by: McLachlan, R., Rynhart, P.
McLachlan, RI. (2003). [Untitled]. Society for Industrial and Applied Mathematics Review. 45(4), 817-821
[Journal article]Authored by: McLachlan, R.
Kathirgamanathan, P., McKibbin, R., & McLachlan, RI. (2003). Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 1: Source at a known location. Research Letters in Informational and Mathematical Sciences. 5, 71-84
[Journal article]Authored by: McLachlan, R.
Kitson, A., McLachlan, RI., & Robidoux, N. (2003). Skew-adjoint finite difference methods on nonuniform grids. New Zealand Journal of Mathematics. 32, 139-159
[Journal article]Authored by: McLachlan, R.
McLachlan, RI. (2003). Spatial discretization of partial differential equations with integrals. IMA Journal of Numerical Analysis. 23(4), 645-664
[Journal article]Authored by: McLachlan, R.
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Kathirgamanathan, P., McKibbin, R., & McLachlan, RI. (2003). Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 2: Source at an unknown location. Research Letters in Information and Mathematical Sciences. 5, 85-118
[Journal article]Authored by: McLachlan, R.
Mclachlan, RI. (2003). [Untitled]. New Zealand Mathematical Society Newsletter. 87, 34-35
[Journal article]Authored by: McLachlan, R.
McLachlan, RI., Perlmutter, M., & Quispel, GRW. (2003). Lie group foliations: Dynamical systems and integrators. Future Generation Computer Systems. 19(7), 1207-1219
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Quispel, GRW. (2003). Geometric integration of conservative polynomial ODEs. Applied Numerical Mathematics. 45(4), 411-418
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Ryland, B. (2003). The algebraic entropy of classical mechanics. Journal of Mathematical Physics. 44(7), 3071-3087
[Journal article]Authored by: McLachlan, R.
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Gascuel, O., Hendy, MD., Jean-Marie, A., & McLachlan, R. (2003). The combinatorics of tandem duplication trees. Systematic Biology. 52(1), 110-118
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (2002). The emerging science of geometric integration. New Zealand Science Review. 59(3&4), 114-115
[Journal article]Authored by: McLachlan, R.
Rynhart, PR., McKibbin, R., McLachlan, RI., & Jones, JR. (2002). Mathematical modelling of granulation: Static and dynamic liquid bridges. Research Letters in the Information and Mathematical Sciences. 3(1), 199-212
[Journal article]Authored by: McLachlan, R., Rynhart, P.
Kathirgamanathan, P., McKibbin, R., & McLachlan, RI. (2002). Source term estimation of pollution from an instantaneous point source. Research Letters in the Information and Mathematical Sciences. 3, 59-67
[Journal article]Authored by: McLachlan, R.
McLachlan, RI., & Quispel, GRW. (2002). Splitting methods. Acta Numerica. 11, 341-434
[Journal article]Authored by: McLachlan, R.
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612
McLachlan, RI. (2002). Families of high-order composition methods. Numerical Algorithms. 31(31), 233-246
[Journal article]Authored by: McLachlan, R.
McLachlan, RI. (2001). [Untitled]. New Zealand Mathematical Society Newsletter. 83, 23-23
[Journal article]Authored by: McLachlan, R.
McLachlan, R., & Perlmutter, M. (2001). Conformal Hamiltonian systems. Journal of Geometry and Physics. 39(4), 276-300
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Quispel, GRW. (2001). What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration. Nonlinearity. 14(6), 1689-1705
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Quispel, GRW. (2000). Numerical integrators that contract volume. Applied Numerical Mathematics. 34(2), 253-260
[Journal article]Authored by: McLachlan, R.
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Iserles, A., McLachlan, R., & Zanna, A. (1999). Approximately preserving symmetries in the numerical integration of ordinary differential equations. European Journal of Applied Mathematics. 10(5), 419-445
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (1999). Area preservation in computational fluid dynamics. Physics Letters A. 264(1), 36-44
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (1999). Area preservation in computational fluid dynamics. Physics Letters, Section A: General, Atomic and Solid State Physics. 264(1), 36-44
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Quispel, GRW., & Robidoux, N. (1999). Geometric integration using discrete gradients. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 357(1754), 1021-1045
[Journal article]Authored by: McLachlan, R.
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394
285
Dupont, F., McLachlan, RI., & Zeitlin, V. (1998). On a possible mechanism of anomalous diffusion by Rossby waves. Physics of Fluids. 10(12), 3185-3193
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Quispel, GRW., & Robidoux, N. (1998). Unified approach to hamiltonian systems, poisson systems, gradient systems, and systems with lyapunov functions or first integrals. Physical Review Letters. 81(12), 2399-2403
[Journal article]Authored by: McLachlan, R.
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Mclachlan, RI., Quispel, GRW., & Turner, GS. (1998). Numerical integrators that preserve symmetries and reversing symmetries. SIAM Journal on Numerical Analysis. 35(2), 586-599
[Journal article]Authored by: McLachlan, R.
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Dullweber, A., Leimkuhler, B., & McLachlan, R. (1997). Symplectic splitting methods for rigid body molecular dynamics. Journal of Chemical Physics. 107(15), 5840-5851
[Journal article]Authored by: McLachlan, R.
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163
McLachlan, RI., Szunyogh, I., & Zeitlin, V. (1997). Hamiltonian finite-dimensional models of baroclinic instability. Physics Letters, Section A: General, Atomic and Solid State Physics. 229(5), 299-305
[Journal article]Authored by: McLachlan, R.
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McLachlan, R. (1995). Comment on "Poisson schemes for Hamiltonian systems on Poisson manifolds". Computers and Mathematics with Applications. 29(3), 1
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (1995). Composition methods in the presence of small parameters. BIT Numerical Mathematics. 35(2), 258-268
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Scovel, C. (1995). Equivariant constrained symplectic integration. Journal of Nonlinear Science. 5(3), 233-256
[Journal article]Authored by: McLachlan, R.
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MCLACHLAN, RI. (1995). ON THE NUMERICAL-INTEGRATION OF ORDINARY DIFFERENTIAL-EQUATIONS BY SYMMETRICAL COMPOSITION METHODS. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 16(1), 151-168
[Journal article]Authored by: McLachlan, R.
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253
MCLACHLAN, R. (1994). THE WORLD OF SYMPLECTIC SPACE. NEW SCIENTIST. 141(1917), 32-35
[Journal article]Authored by: McLachlan, R.
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McLachlan, R. (1994). A gallery of constant-negative-curvature surfaces. The Mathematical Intelligencer. 16(4), 31-37
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Segur, H. (1994). A note on the motion of surfaces. Physics Letters A. 194(3), 165-172
[Journal article]Authored by: McLachlan, R.
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ATELA, P., & MCLACHLAN, RI. (1994). GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES 3-BODY PROBLEM. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 4(4), 865-884
[Journal article]Authored by: McLachlan, R.
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McLachlan, R. (1993). Symplectic integration of Hamiltonian wave equations. Numerische Mathematik. 66(1), 465-492
[Journal article]Authored by: McLachlan, R.
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120
Malmuth, ND., Jafroudi, H., Wu, CC., McLachlan, R., & Cole, JD. (1993). Asymptotic methods for the prediction of transonic wind-tunnel wall interference. AIAA Journal. 31(5), 911-918
[Journal article]Authored by: McLachlan, R.
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1
McLachlan, RI. (1993). Explicit Lie-Poisson integration and the Euler equations. Physical Review Letters. 71(19), 3043-3046
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (1993). Integrable four-dimensional symplectic maps of standard type. Physics Letters A. 177(3), 211-214
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., & Atela, P. (1992). The accuracy of symplectic integrators. Nonlinearity. 5(2), 541-562
[Journal article]Authored by: McLachlan, R.
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294
Mclachlan, R. (1991). A steady separated viscous corner flow. Journal of Fluid Mechanics. 231, 1-34
[Journal article]Authored by: McLachlan, R.
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McLachlan, R. (1991). Comparability of alkaline phosphatase isoenzyme methods [4]. Clinical Chemistry. 37(7), 1301
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI. (1991). The boundary layer on a finite flat plate. Physics of Fluids A. 3(2), 341-348
[Journal article]Authored by: McLachlan, R.
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Callaghan, S., & McLachlan, R. (1990). Affinity blotting: Polyvinyldifluoride (PVDF) is superior to nitrocellulose. Clinical Chemistry. 36(7), 1377
[Journal article]Authored by: McLachlan, R.
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Mclachlan, R., Richardson, GE., & Wolf, MM. (1990). Is igd myeloma a separate clinical entity? report of six cases investigated by isoelectric focusing. Leukemia and Lymphoma. 2(6), 385-390
[Journal article]Authored by: McLachlan, R.
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McLachlan, R. (1989). Monoclonal immunoglobulins: Affinity blotting for low concentrations in serum. Clinical Chemistry. 35(3), 478-481
[Journal article]Authored by: McLachlan, R.
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McLachlan, R., Grigg, AP., Cornell, FN., Harris, RA., & Woodruff, RK. (1988). Demonstration of monoclonal IgE by isoelectric focusing: First reported case of IgE myeloma in Australia. Clinical Chemistry. 34(10), 2168-2171
[Journal article]Authored by: McLachlan, R.
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Braunstein, SL., & McLachlan, RI. (1987). Generalized squeezing. Physical Review A. 35(4), 1659-1667
[Journal article]Authored by: McLachlan, R.
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Nayudu, PL., Gook, D., Lopata, A., Cornell, FN., & McLachlan, R. (1984). A thin鈥恖ayer isoelectric focusing method for the separation of proteins in follicular fluid and seminal plasma. Gamete Research. 9(2), 207-220
[Journal article]Authored by: McLachlan, R.
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Zalcberg, JR., Cornell, FN., Ireton, HJC., McGrath, KM., McLachlan, R., Woodruff, RK., . . . Wiley, JS. (1982). Chronic lymphatic leukemia developing in a patient with multiple myeloma. Immunologic demonstration of a clonally distinct second malignancy. Cancer. 50(3), 594-597
[Journal article]Authored by: McLachlan, R.
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Hogarth, PM., Potter, TA., Cornell, FN., McLachlan, R., & McKenzie, IF. (1980). Monoclonal antibodies to murine cell surface antigens I. Lyt-1.1. Journal of Immunology. 125(4), 1618-1624
[Journal article]Authored by: McLachlan, R.
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48
Grimm, V., McLachlan, RI., McLaren, D., Quispel, GRW., & Schönlieb, C-B.The use of discrete gradient methods for total variation type regularization problems in image processing.
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI.Integrable four-dimensional symplectic maps of standard type. Retrieved from http://dx.doi.org/10.1016/0375-9601(93)90027-W
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI., Quispel, GRW., & Robidoux, N.A unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions and/or first integrals. Retrieved from http://dx.doi.org/10.1103/PhysRevLett.81.2399
[Journal article]Authored by: McLachlan, R.
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McLachlan, RI.Explicit Lie-Poisson integration and the Euler equations. Retrieved from http://dx.doi.org/10.1103/PhysRevLett.71.3043
[Journal article]Authored by: McLachlan, R.
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Book

McLachlan, RI., & Quispel, GR. (2001). Six Lectures on Geometric Integration of ODEs. In R. DeVore, A. Iserles, & E. Suli (Eds.) Foundations of Computational Mathematics. (pp. 155 - 210). Cambridge, UK: Cambridge University Press
[Chapter]Authored by: McLachlan, R.

Report

McLachlan, RI.(2003). The stars in their courses: 300 years of geometric integration. Palmerston Noth, NZ: 黑料网, Institute of Fundamental Sciences
[Technical Report]Authored by: McLachlan, R.

Conference

Brown, RG., Mclachlan, R., & marsland, S. (2015, December). Differential invariant signatures for images. Presented at New Zealand Mathematics Colloquium 2015. Christchurch, New Zealand.
[Conference Oral Presentation]Authored by: Brown, R., McLachlan, R.
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Celledoni, E., McLachlan, RI., Owren, B., & Quispel, GRW.Structure of B-series for some classes of geometric integrators. AIP Conference Proceedings. (pp. 739 - 742). 0094-243X.
[Conference]Authored by: McLachlan, R.
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Celledoni, E., McLachlan, R., Owren, B., & Quispel, G. (2009). Structure of B-series for some classes of geometric integrators. Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. Vol. 1 and 2
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
Celledoni, E., Baken, DM., McLachlan, RI., Owren, B., Quispel, G., & Wright, W.(2008). Energy-Preserving Methods and B-Series. . Trondheim, Norway
[Conference Paper]Authored by: Baken, D., McLachlan, R.
Marsland, S., & McLachlan, R. (2007). A hamiltonian particle method for diffeomorphic image registration. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4584 LNCS (pp. 396 - 407).
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
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Marsland, S., & McLachlan, R. (2007). A hamiltonian particle method for diffeomorphic image registration. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4584 LNCS (pp. 396 - 407).
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
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McLachlan, RI., & Marsland, S. (2007). Discrete mechanics and optimal control for image registration. ANZIAM Journal. Vol. 48 (pp. 1 - 16). Australia: 13th Biennial Computational Techniques and Applications Conference [CTAC 2006]
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
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Rynhart, PR., McLachlan, RI., Jones, JR., & McKibbin, R. (2006, April). Extension to Smoluchowski's population balance equation to include liquid binder. Presented at 5th World Congress on Particle Technology. Orlando, FL.
[Conference Oral Presentation]Authored by: McLachlan, R., Rynhart, P.
Rynhart, PR., McLachlan, RI., Jones, JR., & McKibbin, R. (2006). Extension to Smoluchowski's population balance equation to include liquid binder. AIChE Annual Meeting, Conference Proceedings.
[Conference Paper in Published Proceedings]Authored by: McLachlan, R., Rynhart, P.
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McLachlan, RI., & Marsland, S. (2007). Discrete mechanics and optimal control for image registration. In ANZIAM Journal Vol. 48 (pp. C1 - C13).
[Conference Abstract]Authored by: McLachlan, R.
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10
Li, X., Flenley, JR., Rapson, GL., & Mclachlan, RI. (2004). Interpreting vegetation dynamics with pollen data from undisturbed and disturbed sites in New Zealand. Poster session presented at the meeting of 47th Annual Meeting of International Association of Vegetation Science. Kailua-Kona, Hawaii
[Conference Poster]Authored by: Li, X., McLachlan, R.
McLachlan, RI. (2004, November). Another good reason to arrange points on a sphere. Presented at Mathematics Colloquium. University of Auckland, Auckland, NZ.
[Conference Oral Presentation]Authored by: McLachlan, R.
McLachlan, RI. (2004, February). Geometric numerical integration. Presented at Victoria International Conference 2004. Victoria University of Wellington, Wellington, NZ.
[Conference Oral Presentation]Authored by: McLachlan, R.
Rynhart, PR., McLachlan, RI., & McKibbin, R. (2003, July). Liquid bridges between three particles. Presented at 5th International Congress on Industrial and Applied Mathematics. Sydney, NSW.
[Conference Oral Presentation]Authored by: McLachlan, R., Rynhart, P.
Kathirgamanathan, P., McKibbin, R., & McLachlan, RI. (2003). Inverse modelling for identifying the origin and release rate of atmospheric pollution - an optimisation approach. (pp. 64 - 69). , MODSIM 2003 International Congress on Modelling and Simulation Canberra, ACT: Modelling and Simulation Society of Australia and New Zealand
[Conference Abstract]Authored by: McLachlan, R.
Li, X., Flenley, JR., Rapson, GL., & Mclachlan, RI. (2003, November). Testing vegetation dynamics around sponge swamp and Tiniroto Lakes: A numerical analysis. Presented at New Zealand Ecological Society Conference. University of Auckland, Auckland, NZ.
[Conference Oral Presentation]Authored by: McLachlan, R.
Rynhart, PR., McLachlan, RI., Jones, JR., & McKibbin, R. (2003). Solution of the Young-Laplace equation for three particles. In QD. Nguyen, PJ. Ashman, K. Quast, & NS. Eds (Eds.) CHEMECA 2003: 31st Australasian Chemical Engineering Conference: Proceedings. (pp. unpaged). Adelaide, SA
[Conference Paper in Published Proceedings]Authored by: McLachlan, R., Rynhart, P.
Kathirgamanathan, P., McKibbin, R., & McLachlan, RI. (2003). Inverse modelling for identifying the origin and release rate of atmospheric pollution - An optimisation approach. MODSIM 2003: INTERNATIONAL CONGRESS ON MODELLING AND SIMULATION, VOLS 1-4. (pp. 64 - 69). : International Congress on Modelling and Simulation
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
McLachlan, RI.Families of high-order composition methods. Numerical Algorithms. 31 (1-4)(pp. 233 - 246). 1017-1398.
[Conference]Authored by: McLachlan, R.
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Rynhart, PR., & McLachlan, RI. (2002, December). Liquid bridges between three particles. Presented at New Zealand Mathematics Colloquium 2002. University of Auckland, Auckland, NZ.
[Conference Oral Presentation]Authored by: McLachlan, R., Rynhart, P.
Rynhart, PR., McKibbin, R., McLachlan, RI., & Jones, JR. (2002). Mathematical modelling of granulation: Static and dynamic liquid bridges. In JL. Ed (Ed.) 4th World Congress on Particle Technology: Proceedings. (pp. unpaged). Sydney, NSW
[Conference Paper in Published Proceedings]Authored by: McLachlan, R., Rynhart, P.
Kathirgamanthan, P., McKibbin, R., & McLachlan, RI. (2001). Source term estimation of pollution from an instantaneous point source. In F. Ghassemi, P. Whetton, R. Little, & M. Littleboy (Eds.) MODSIM 2001, International Congress on Modelling and Simulation. Vol. Part 2 (pp. 1013 - 1018). Canberra, ACT
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
McLachlan, RI., & Robidoux, N. (2000). Antisymmetry, pseudo-spectral methods, and conservative PDEs. In B. Fiedler, K. Groger, & JS. Eds (Eds.) International Conference on Differential Equations. Vol. 2 (pp. 994 - 999). Singapore
[Conference Paper in Published Proceedings]Authored by: McLachlan, R.
Dupont, F., McLachlan, RI., & Zeitlin, V.(1998, March). On a possible mechanism of anomalous diffusion in geophysical turbulence. FUNDAMENTAL PROBLEMATIC ISSUES IN TURBULENCE. (pp. 203 - 209).
[Conference]Authored by: McLachlan, R.
McLachlan, RI., & Quispel, GRW.Generating functions for dynamical systems with symmetries, integrals, and differential invariants. Physica D: Nonlinear Phenomena. 112 (1-2)(pp. 298 - 309). 0167-2789.
[Conference]Authored by: McLachlan, R.
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McLachlan, RI., & Gray, SK.Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation. Applied Numerical Mathematics. 25 (2-3)(pp. 275 - 286). 0168-9274.
[Conference]Authored by: McLachlan, R.
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Malmuth, ND., Jafroudi, H., Wu, CC., McLachlan, R., & Cole, JD.Asymptotic methods for the prediction of transonic wind tunnel wall interference. AIAA 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1991.
[Conference]Authored by: McLachlan, R.
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Other

Marsland, SR., & McLachlan, RI. (2007, July). Numerical methods for shape analysis. In Summer Program on the Geometry and Statistics of Shape Spaces. Presented at Research Triangle Park, NC.
[Oral Presentation]Authored by: McLachlan, R.
McLachlan, RI. (2004). Holonomy and hammers. Secondary School Mathematics Teachers' Evening
[Other]Authored by: McLachlan, R.

Teaching and Supervision

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Co-supervisor 0 10

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