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.Read Online:
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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.Read Online:
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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.Read article at Massey Research Online:
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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.Read article at Massey Research Online:
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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.Read article at Massey Research Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read article at Massey Research Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Online:
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Oneale, DRJ., & McLachlan, RI. (2009). Reconsidering trigonometric integrators.
ANZIAM Journal. 50(3), 320-332
[Journal article]Authored by: McLachlan, R.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Online:
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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Online:
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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.Read Online:
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.Read Abstract:
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.Read Abstract:
McLachlan, R., & Perlmutter, M. (2006). Integrators for nonholonomic mechanical systems.
Journal of Nonlinear Science. 16(4), 283-328
[Journal article]Authored by: McLachlan, R.Read Abstract:
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.
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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
McLachlan, RI., & Quispel, GRW. (2003). Geometric integration of conservative polynomial ODEs.
Applied Numerical Mathematics. 45(4), 411-418
[Journal article]Authored by: McLachlan, R.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
McLachlan, RI., & Quispel, GRW. (2000). Numerical integrators that contract volume.
Applied Numerical Mathematics. 34(2), 253-260
[Journal article]Authored by: McLachlan, R.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Online:
McLachlan, RI. (1995). Composition methods in the presence of small parameters.
BIT Numerical Mathematics. 35(2), 258-268
[Journal article]Authored by: McLachlan, R.Read Online:
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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.Read Online:
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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.Read Online:
MCLACHLAN, R. (1994). THE WORLD OF SYMPLECTIC SPACE.
NEW SCIENTIST. 141(1917), 32-35
[Journal article]Authored by: McLachlan, R.
McLachlan, R. (1994). A gallery of constant-negative-curvature surfaces.
The Mathematical Intelligencer. 16(4), 31-37
[Journal article]Authored by: McLachlan, R.Read Online:
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.Read Online:
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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.Read Online:
McLachlan, R. (1993). Symplectic integration of Hamiltonian wave equations.
Numerische Mathematik. 66(1), 465-492
[Journal article]Authored by: McLachlan, R.Read Online:
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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.Read Online:
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McLachlan, RI. (1993). Explicit Lie-Poisson integration and the Euler equations.
Physical Review Letters. 71(19), 3043-3046
[Journal article]Authored by: McLachlan, R.Read Online:
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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.Read Online:
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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.Read Online:
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Mclachlan, R. (1991). A steady separated viscous corner flow.
Journal of Fluid Mechanics. 231, 1-34
[Journal article]Authored by: McLachlan, R.Read Online:
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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.Read Online:
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.Read Online:
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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.Read Online:
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.Read Online:
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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.Read Online:
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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.Read Online:
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Braunstein, SL., & McLachlan, RI. (1987). Generalized squeezing.
Physical Review A. 35(4), 1659-1667
[Journal article]Authored by: McLachlan, R.Read Online:
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Nayudu, PL., Gook, D., Lopata, A., Cornell, FN., & McLachlan, R. (1984). A thin‐layer 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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Abstract:
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.Read Online:
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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.Read Abstract:
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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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Abstract:
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.Read Online:
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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.Read Online:
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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.Read Online:
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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.Read Abstract:
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