{"id":5,"date":"2026-01-20T15:33:04","date_gmt":"2026-01-20T02:33:04","guid":{"rendered":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/?page_id=5"},"modified":"2026-01-20T15:33:04","modified_gmt":"2026-01-20T02:33:04","slug":"publications-of-robert-i-mclachlan","status":"publish","type":"page","link":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/publications-of-robert-i-mclachlan\/","title":{"rendered":"Publications of Robert I McLachlan"},"content":{"rendered":"\n
    \n
  1. H. Barr, M. A. Grant, and R. I. McLachlan, Proving and development of geothermal fields — risk, strategy and economics, Applied Mathematics Division Report 116, Department of Scientific and Industrial Research, Wellington, New Zealand, 1984.<\/li>\n\n\n\n
  2. S. L. Braunstein and R. I. McLachlan, Generalized squeezing<\/a>, Phys. Rev. A 35(4) (1987), 1659-1667.<\/li>\n\n\n\n
  3. N. D. Malmuth, C. C. Wu, H. Jafroudi, R. I. McLachlan, J. D. Cole, and R. Sahu, Asymptotic theory of transonic wind tunnel wall interference<\/a>, Arnold Engineering Development Center report SC5413.FR., 1990. <\/li>\n\n\n\n
  4. R. I. McLachlan, Separated viscous flows via multigrid<\/a>, Ph.D. thesis, Caltech (1990).<\/li>\n\n\n\n
  5. R. I. McLachlan, A steady separated viscous corner flow<\/a>, J. Fluid Mech. 231 (1991), 1-34. <\/li>\n\n\n\n
  6. R. I. McLachlan, The boundary layer on a finite flat plate<\/a>, Phys. Fluids A 3(1) (1991), 341-438.<\/li>\n\n\n\n
  7. R. I. McLachlan, On visualizing the four-dimensional rigid body<\/a>, Program in Applied Mathematics Report 141, U. Colorado at Boulder, 1992. <\/li>\n\n\n\n
  8. R. I. McLachlan and P. Atela, The accuracy of symplectic integrators<\/a>, Nonlinearity 5 (1992), 541-562.<\/li>\n\n\n\n
  9. R. I. McLachlan, Multigrid solution of the Navier-Stokes equations at high Reynolds numbers, Program in Applied Mathematics report 167, U. Colorado at Boulder, 1993. <\/li>\n\n\n\n
  10. P. Atela and R. I. McLachlan, A note on the charged isosceles three-body problem<\/a>, Proc. Int. Conf. Diff. Eqs. EQUADIFF 91 pp. 292-297, C. Perello, C. Simo, and J. Sola-Morales, eds., World Scientific, Singapore, 1993. <\/li>\n\n\n\n
  11. N. D. Malmuth, H. Jafroudi, C. C. Wu, R. I. McLachlan, and J. D. Cole, Asymptotic methods for the prediction of transonic wind-tunnel wall interference<\/a>, AIAA J. 31(5) (1993), 911-918. <\/li>\n\n\n\n
  12. R. I. McLachlan, Integrable four-dimensional symplectic maps of standard type<\/a>, Phys. Lett. A. 173(3) (1993), 211-214. <\/li>\n\n\n\n
  13. R. I. McLachlan, Explicit symplectic splitting methods applied to PDE’s<\/a>, Proc. AMS-SIAM Conf. Exploiting Symmetry in Applied Mathematics, Lects. Appl. Math. 29, AMS, 1993, pp. 325-337. <\/li>\n\n\n\n
  14. R. I. McLachlan, Explicit Lie-Poisson integration and the Euler equations<\/a>, Phys. Rev. Lett. 71 (1993), 3043-3046. <\/li>\n\n\n\n
  15. R. I. McLachlan, A gallery of constant-negative-curvature surfaces<\/a>, The Mathematical Intelligencer 16(4) (1994), 31-37. <\/li>\n\n\n\n
  16. R. I. McLachlan, Symplectic integration of Hamiltonian wave equations<\/a>, Numer. Math. 66 (1994) 465-492 <\/li>\n\n\n\n
  17. R. I. McLachlan, The world of symplectic space<\/a>, New Scientist, 19 March 1994, 32-35. <\/li>\n\n\n\n
  18. R. I. McLachlan and H. Segur, A note on the motion of surfaces<\/a>, Phys. Lett. A 194(3) (1994), 165-172. <\/li>\n\n\n\n
  19. P. Atela and R. I. McLachlan, Global behaviour of the charged isosceles three-body problem<\/a>, Int. J. Bifurcations Chaos 4(4) (1994), 865-884.<\/li>\n\n\n\n
  20. R. I. McLachlan and C. Scovel, Equivariant constrained symplectic integration<\/a>, J. Nonlinear Sci. 5 (1995), 233-256. <\/li>\n\n\n\n
  21. R. I. McLachlan, On the numerical integration of ordinary differential equations by symmetric composition methods<\/a>, SIAM J. Sci. Comp. 16, (1995), 151-168. <\/li>\n\n\n\n
  22. R. I. McLachlan, Comment on “Poisson schemes for Hamiltonian systems on Poisson manifolds<\/a>“<\/a>, Comp. Math. App. 29(3) (1995), 1. <\/li>\n\n\n\n
  23. R. I. McLachlan, Composition methods in the presence of small parameters<\/a>, BIT 35(2) (1995), 258-268. <\/li>\n\n\n\n
  24. R. I. McLachlan, More on symplectic correctors<\/a>, in Integration Algorithms and Classical Mechanics, J.E. Marsden, G.W. Patrick, and W.F. Shadwick, eds., AMS, 1996, pp. 141-149. <\/li>\n\n\n\n
  25. R. I. McLachlan and C. Scovel, Open problems in symplectic integration<\/a>, in Integration Algorithms and Classical Mechanics, J.E. Marsden, G.W. Patrick, and W.F. Shadwick, eds., AMS, 1996, pp. 151-180.<\/li>\n\n\n\n
  26. R. I. McLachlan and G. R. W. Quispel, Generating functions for dynamical systems with symmetries, integrals, and differential invariants<\/a>, Physica D 112 (1,2) (1997), 298-309. <\/li>\n\n\n\n
  27. R. I. McLachlan and S. Gray, Optimal stability polynomials for splitting methods, with application to the time-dependent Schrodinger equation<\/a>, Appl. Numer. Anal. 25 (1997), 275-286. <\/li>\n\n\n\n
  28. A. Dullweber, B. Leimkuhler, and R. I. McLachlan, Symplectic splitting methods for rigid body molecular dynamics<\/a>, J. Chem. Phys. 107(5) (1997), 5840-5851. <\/li>\n\n\n\n
  29. R. I. McLachlan, I. Szunyogh, and V. Zeitlin, Hamiltonian finite-dimensional models of baroclinic instability<\/a>, Phys. Lett. A 229(5) (1997), 299-306. <\/li>\n\n\n\n
  30. R. I. McLachlan, G. R. W. Quispel, and G. S. Turner, Numerical integrators that preserve symmetries and reversing symmetries<\/a>, SIAM J. Numer. Anal. 35 (1998), 586-599. <\/li>\n\n\n\n
  31. F. Dupont, R. I. McLachlan, and V. Zeitlin, On a possible mechanism of anomalous diffusion by Rossby waves<\/a>, Phys. Fluids 10(12) (1998), 3185-3193. <\/li>\n\n\n\n
  32. R. I. McLachlan, G. R. W. Quispel, and N. Robidoux, Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals<\/a>, Phys. Rev. Lett. 81 (1998), 2399-2403. <\/li>\n\n\n\n
  33. F. Dupont, R. I. McLachlan, and V. Zeitlin, On a possible mechanism of anomalous diffusion in geophysical turbulence<\/a>, Fundamental problematic issues in turbulence (Monte Verita, 1998), pp. 203-209, Trends Math., Birkhauser, Basel, 1999. <\/li>\n\n\n\n
  34. R. I. McLachlan, G. R. W. Quispel, and N. Robidoux, Geometric integration using discrete gradients<\/a>, Phil. Trans. Roy. Soc. A 357 (1999), 1021-1046. <\/li>\n\n\n\n
  35. A. Iserles, R. I. McLachlan, and A. Zanna, Approximately preserving symmetries in the numerical integration of ordinary differential equations<\/a>, Eur. J. Appl. Math. 10(5) (1999), 419-445. <\/li>\n\n\n\n
  36. R. I. McLachlan, Area preservation in computational fluid dynamics<\/a>, Phys. Lett. A 264 (1999), 36-44. <\/li>\n\n\n\n
  37. R. I. McLachlan and G. R. W. Quispel, Numerical integrators that contract volume<\/a>, Appl. Numer. Math. 34 (2000), 253-260. <\/li>\n\n\n\n
  38. R. I. McLachlan and N. Robidoux, Antisymmetry, pseudospectral methods, and conservative PDEs<\/a>, EQUADIFF 99, B. Fiedler, K. Groger, and J. Sprekels, eds., World Scientific, 2000, pp. 994-999.<\/li>\n\n\n\n
  39. R. I. McLachlan and N. Robidoux, Antisymmetry, pseudospectral methods, weighted residual discretizations, and energy conserving partial differential equations<\/a> (2000), preprint.<\/li>\n\n\n\n
  40. R. I. McLachlan and G. R. W. Quispel, Six Lectures on Geometric Integration<\/a>, in Foundations of Computational Mathematics pages 155-210, ed. R. DeVore, A. Iserles, E. Suli, Cambridge University Press, Cambridge, 2001. <\/li>\n\n\n\n
  41. R. I. McLachlan and G. R. W. Quispel, What kinds of dynamics are there? Lie pseudogroups, dynamical systems, and geometric integration<\/a>, Nonlinearity 14 (2001), 1689-1705. <\/li>\n\n\n\n
  42. R. I. McLachlan and M. Perlmutter, Conformal Hamiltonian systems<\/a>, J. Geom. Phys. 39(4) (2001), 276-300. <\/li>\n\n\n\n
  43. P. Kathirgamanathan, R. McKibbin and R. I. McLachlan, Source term estimation of pollution from an instantaneous point source<\/a>, in MODSIM 2001, International Congress on Modelling and Simulation pp. 1013-1018, F. Ghassemi, P. Whetton, R. Little, and M. Littleboy, eds., Modelling and Simulation Society of Australia and New Zealand, Inc., 2001.<\/li>\n\n\n\n
  44. R. I. McLachlan, Families of high-order composition methods<\/a>, Numerical Algorithms 31, (2002), 233-246. <\/li>\n\n\n\n
  45. R. I. McLachlan and G. R. W. Quispel, Splitting methods<\/a>, Acta Numerica 11 (2002), 341-434. <\/li>\n\n\n\n
  46. P. Rynhart, R. McLachlan, R. McKibbin, and J. R. Jones, Mathematical modelling of granulation: Static and dynamic liquid bridges<\/a>, Proceedings of the Fourth World Congress on Particle Technology (WCPT4), Sydney, 2002. <\/li>\n\n\n\n
  47. O. Gascuel, M. D. Hendy, A. Jean-Marie and R. McLachlan, The combinatorics of tandem duplication trees<\/a>, Syst. Biol. 52 (2003), 110-118. <\/li>\n\n\n\n
  48. R. I. McLachlan, M. Perlmutter, and G. R. W. Quispel, Lie group foliations: Dynamical systems and integrators<\/a>, Future Generation Computer Systems, 19 (2003) 1207-1219. <\/li>\n\n\n\n
  49. R. I. McLachlan, The emerging science of geometric integration, New Zealand Science Review, 2003.<\/li>\n\n\n\n
  50. R. I. McLachlan and G. R. W. Quispel, Geometric integration of conservative polynomial ODEs<\/a>, Appl. Numer. Math. 45 (2003), 411-418. <\/li>\n\n\n\n
  51. R. I. McLachlan and B. N. Ryland, The algebraic entropy of classical mechanics<\/a>, J. Math. Phys. 44 (2003), 3071-3087. <\/li>\n\n\n\n
  52. R. I. McLachlan, Spatial discretization of PDEs with integrals<\/a>, IMA J. Numer. Anal. 23 (2003), 645-664. <\/li>\n\n\n\n
  53. A. Kitson, R. I. McLachlan, and N. Robidoux, Skew-adjoint finite difference methods on nonunform grids<\/a>, New Zealand J. Math., 32 (2003) 139-159. <\/li>\n\n\n\n
  54. Book review of Geometric Numerica<\/em>l Integration<\/em> by E Hairer, Ch Lubich, and G Wanner, SIAM Featured Review<\/a> 45 (2003), 817-821. <\/li>\n\n\n\n
  55. P Kathirgamanathan, R McKibbin, and R I McLachlan (2003). Inverse modelling for identifying the origin and release rate of atmospheric pollution: An optimisation approach<\/a>. in MODSIM 2003: International Congress on Modelling and Simulation: Proceedings (Volume 1), Modelling and Simulation Society of Australia and New Zealand, Canberra, ACT. pp. 64–69. <\/li>\n\n\n\n
  56. P R Rynhart, R I McLachlan, J R Jones, and R McKibbin, R. (2003). Solution of the Young-Laplace equation for three particles<\/a>. Q.D. Nguyen, P.J. Ashman, K. Quast, & N. Swain (Eds.) in CHEMECA 2003: 31st Australasian Chemical Engineering Conference: Proceedings, University of Adelaide, Institution of Engineers, Adelaide, SA. <\/li>\n\n\n\n
  57. U. Ascher and R. I. McLachlan, Multisymplectic box schemes and the Korteweg-de Vries equation<\/a>, Appl. Numer. Math. 48 (2004), 255-269. <\/li>\n\n\n\n
  58. R. I. McLachlan and G. R. W. Quispel, Explicit geometric integration of polynomial vector fields<\/a>, BIT 44 (2004), 515-538. <\/li>\n\n\n\n
  59. R. I. McLachlan, M. Perlmutter, and G. R. W. Quispel, On the nonlinear stability of symplectic integrators<\/a>, BIT 44 (2004), 99-117. <\/li>\n\n\n\n
  60. R. I. McLachlan and M. Perlmutter, Energy drift in reversible time integration<\/a>, J. Phys. A 37(45) (2004), L593-L598.<\/li>\n\n\n\n
  61. R. I. McLachlan and A. Zanna, The discrete Moser-Veselov algorithm for the free rigid body, revisited<\/a>, Foundations of Comput. Math. 5 (2005), 87-123. <\/li>\n\n\n\n
  62. U. Ascher and R. I. McLachlan, O<\/a>n sy<\/a>mplectic and multisymplectic schemes for the KdV equations<\/a>, J. Sci. Comput., 25 (1) (2005) 83-104. <\/li>\n\n\n\n
  63. I G Mason, R I McLachlan and D T Gerard, A doubl<\/a>e exponential model for biochemical oxygen demand<\/a>, Bioresource Technology 97 (2) (2006), 273-282. <\/li>\n\n\n\n
  64. R I McLachlan and G R W Quispel, Ge<\/a>om<\/a>etric integrators for ODEs<\/a>, J. Phys. A 39(19) 2006, 5251-5286. <\/li>\n\n\n\n
  65. R McLachlan and S Marsland, Kelvin–Helm<\/a>holt<\/a>z instability of momentum sheets in the Euler equations for planar diffeomorphisms<\/a>, SIAM J. Appl. Dyn. Sys. 5 (2006), 726–758. <\/li>\n\n\n\n
  66. R I McLachlan and D R O’Neale, Geometric integra<\/a>tio<\/a>n for a two-spin system<\/a>, J. Phys. A: Math. Gen. 39 (2006) L447-L452. <\/li>\n\n\n\n
  67. R I McLachlan and M Perlmutter, Integrators for nonholonomic mechanical systems<\/a>, J Nonlinear Sci 16(4) (2006), 283-328. <\/li>\n\n\n\n
  68. R I McLachlan and S R Marsland, Discrete m<\/a>echan<\/a>ics and optimal control for image registration<\/a>, ANZIAM J., 2006, vol 48, Electronic supplement 2006–2007, pp. C1-C16. <\/li>\n\n\n\n
  69. G R W Quispel and R I McLachlan, eds., J Phys A, Special issue on Geometric Numerical Integration<\/a>, 39(19) (2006), 5251–5652. <\/li>\n\n\n\n
  70. R. I. McLachlan, Integration and applications of generalized Euler equations. In E~Hairer, editor, Geometric Numerical Integration, Oberwolfach Report 14\/2006, pages 68–70, 2006.<\/li>\n\n\n\n
  71. R I McLachlan, A new implementation of symplectic Runge-Kutta methods<\/a>, SIAM J Sci Comput 29(4) 2007, 1637-1649. <\/li>\n\n\n\n
  72. R. I. McLachlan and S. R. Marsland, N-particle dynamics of the Euler equations for planar diffeomorphisms<\/a>. Dynamical Systems <\/em>22(3) 2007, 269-290. <\/li>\n\n\n\n
  73. Ryland B.N., McLachlan, R.I., and Frank, J., On multisymplecticity of partitioned Runge-Kutta and splitting methods<\/a>, Int J Comput Math<\/em>, 84(6) 2007, 847-869. <\/li>\n\n\n\n
  74. S Marsland and RI McLachlan, A Hamiltonian particle method for diffeomorphic image registration<\/a>. In Proceedings of Information Processing in Medical Images<\/em>, volume 4548 of Lecture Notes in Computer Science<\/em>, pages 396-407. Springer, 2007.<\/li>\n\n\n\n
  75. Ryland B.N., McLachlan R.I., On multisymplecticity of partitioned Runge-Kutta methods<\/a>, SIAM J. Sci. Comput. <\/em>30(3) 2008, 1318-1340. <\/li>\n\n\n\n
  76. Hairer E, McLachlan, R I, Razakarivony A, Achieving Brouwer’s law with implicit Runge-Kutta methods<\/a>, BIT<\/em> 48(2) 2008, 231-244. <\/li>\n\n\n\n
  77. McLachlan, R.I., H Z Munthe-Kaas, G R W Quispel, and A Zanna, Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields<\/a>, Foundations Comput. Math.<\/em> 8 2008, 335-355. <\/li>\n\n\n\n
  78. E Celledoni, R I McLachlan, D I McLaren, B Owren, G R W Quispel, and W Wright, Energy-preserving methods and B-series<\/a>, Proc. 21st<\/sup> Nordic Seminar on Computational Mathematics<\/em>, 2008, 4pp.<\/li>\n\n\n\n
  79. E Hairer, R I McLachlan, and R D Skeel, On energy behaviour of the modified Takahashi-Imada method<\/a>, Mathematical Modelling and Numerical Analysis <\/em>43 (2009) 631-644. <\/li>\n\n\n\n
  80. E Celledoni, R I McLachlan, D I McLaren, B Owren, G R W Quispel, and W Wright, Energy-preserving Runge-Kutta methods<\/a>, Mathematical Modelling and Numerical Analysis<\/em> 43 (2009) 645-649. <\/li>\n\n\n\n
  81. R I McLachlan, G R W Quispel, and P S P Tse, Linearization-preserving self-adjoint and symplectic integrators<\/a>, BIT<\/em> 49(1) (2009), 177-197. <\/li>\n\n\n\n
  82. R I McLachlan, The structure of a set of vector fields on Poisson manifolds<\/a>, J. Phys. A: Math. Theor. <\/em>42 (2009) 142001. <\/li>\n\n\n\n
  83. R I McLachlan and X Zhang, Well-posedness of modified Camassa-Holm equations<\/a>, J. Differential Equations<\/em> 246 (2009) 3241-3259. <\/li>\n\n\n\n
  84. A J Elvin, C R Laing, R I McLachlan, and M G Roberts, Exploiting the Hamiltonian structure of a neural field model<\/a>, Physica D<\/em> (2009), in press. <\/li>\n\n\n\n
  85. D R O’Neale and R I McLachlan, Reconsidering trigonometric integrators<\/a>, ANZIAM Journal<\/em> 50 (2009), 3241-3259.<\/li>\n\n\n\n
  86. D R J O’Neale and R I McLachlan, Preservation and destruction of periodic orbits by symplectic integrators<\/a>, Numerical Algorithms 53 (2010), 343-362. <\/li>\n\n\n\n
  87. E Celledoni, R I McLachlan, B Owren, and G R W Quispel, On conjugate B-series and their geometric structure<\/a>, Journal of Numerical Analysis, Industrial and Applied Mathematics 5 (2010), 343-362. <\/li>\n\n\n\n
  88. E Celledoni, R I McLachlan, B Owren, and G R W Quispel, Energy-preserving integrators and the structure of B-series<\/a>, Foundations of Computational Mathematics, 10 (2010) 673-693. <\/li>\n\n\n\n
  89. R McLachlan and X Zhang, Dynamics of the generalized Euler equations on Virasoro groups<\/a>, (2010), preprint.<\/li>\n\n\n\n
  90. K Modin, M Perlmutter, S Marsland, R McLachlan, Geodesics on Lie groups: Euler equations and totally geodesic subgroups<\/a>, Res. Lett. Inf. Math. Sci., Massey University 14 (2010), 79-106.<\/li>\n\n\n\n
  91. R I McLachlan, Y Sun, and P S P Tse, Linear stability of partitioned Runge-Kutta methods<\/a>, SIAM J Numer. Anal., 49 (2011), 232-263. <\/li>\n\n\n\n
  92. K Modin, M Perlmutter, S R Marsland, and R I McLachlan, On Euler-Arnold equations and totally geodesic subgroups<\/a>,<\/a> J Geom Phys 61 (2011), 1446-1461. <\/li>\n\n\n\n
  93. R I McLachlan and X Y Zhang, Asymptotic profiles for modified Camassa-Holm equations<\/a>, SIAM J Appl. Dyn. Sys. 10 (2011), 452-468. <\/li>\n\n\n\n
  94. S Marsland, R McLachlan, K Modin, and M Perlmutter, On a geodesic equation for planar conformal template matching<\/a>, Proc. Third Int. Workshop Mathematical Foundations of Computational Anatomy – Geometrical and Statistical Methods for Modelling Biological Shape Variability (2011), 52-63.<\/li>\n\n\n\n
  95. S Marsland, R I McLachlan, K Modin, and M Perlmutter, Geodesic warps by conformal mappings<\/a>, International Journal of Computer Vision, Vision (2012), 1-11, DOI 10.1007\/s11263-012-0584-x. <\/a><\/li>\n\n\n\n
  96. E Celledoni, V Grimm, R I McLachlan, D I McLaren, D R J O’Neale, B Owren, and G R W Quispel, <\/a>Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method<\/a>, J Comput Phys, 231 (2012), 6770-6789.<\/li>\n\n\n\n
  97. E Celledoni, R I McLachlan, G R W Quispel, and B Owren, Geometric properties of Kahan’s method<\/a>, J. Phys. A 46(2) (2013), 025201 <\/li>\n\n\n\n
  98. R I McLachlan, K Modin, O Verdier, and M Wilkins, Symplectic integrators for index one constraints<\/a>, SIAM J Sci Comput 35(5) (2013), A2150-A2162.<\/li>\n\n\n\n
  99. R I McLachlan and G R W Quispel, Discrete gradient methods have an energy conservation law<\/a>, Disc. Cont. Dyn. S. A, 34(3) (2014), 1099-1104. doi:10.3934\/dcds.2014.34.1099 <\/li>\n\n\n\n
  100. S Marsland, R McLachlan, K Modin, and M Perlmutter, On conformal variational problems and free boundary continua<\/a>, J. Phys. A 47 (2014) 145204. <\/li>\n\n\n\n
  101. R I McLachlan, K Modin, and O Verdier, Collective symplectic integrators<\/a>, Nonlinearity 27(6) (2014), 1525-1542. <\/li>\n\n\n\n
  102. R I McLachlan, K Modin, and O Verdier, Collective Lie-Poisson integrators on R^3<\/a>, IMA J. Numer. Anal. (2014). <\/li>\n\n\n\n
  103. R I McLachlan and A Stern, Modified trigonometric integrators<\/a>, SIAM J. Numer. Anal. 52(3) (2014), 1378-1397. <\/li>\n\n\n\n
  104. R I McLachlan, K Modin, O Verdier, and M Wilkins, Geometric generalisations of SHAKE and RATTLE<\/a>, Foundations of Computational Mathematics 14 (2014), 339-370. <\/li>\n\n\n\n
  105. R I McLachlan, K Modin, and O Verdier, Symplectic integrators for spin systems<\/a>, Phys. Rev. E 89(6), 061301, 2014. <\/li>\n\n\n\n
  106. R I McLachlan, B N Ryland, and Y Sun, High order multisymplectic Runge-Kutta methods<\/a>, SIAM J. Sci. Comput. 36(5), A2199-A2226, 2014. <\/li>\n\n\n\n
  107. E Celledoni, R I McLachlan, D I McLaren, B Owren, and G R W Quispel, Integrability properties of Kahan’s method<\/a>, J Phys. A 47(36) (2014) 365202.<\/li>\n\n\n\n
  108. R I McLachlan and M C Wilkins, The multisymplectic diamond scheme,<\/a> SIAM J Sci. Comput. 37(1) (2015) A369-A390. <\/li>\n\n\n\n
  109. R I McLachlan, K Modin, H Munthe-Kaas, and K Modin, B-series are exactly the affine equivariant methods<\/a>, Numer. Math. 133 (2016), 599-622. <\/li>\n\n\n\n
  110. E Celledoni, R I McLachlan, D I McLaren, B Owren, and G R W Quispel, Discretization of polynomial vector fields by polarization<\/a> Proc. Roy. Soc. A 471: 20150390.<\/li>\n\n\n\n
  111. R I McLachlan, K Modin, and O Verdier, Geometry of discrete-time spin systems<\/a>, J. Nonlinear Sci. 26(5) (2016), 1507-1523. <\/li>\n\n\n\n
  112. S Marsland and R I McLachlan, M\u00f6bius invariants of shapes and images<\/a>, Symmetry, Integrability and Geometry: Methods and Applications, SIGMA 12 (2016), 080. <\/li>\n\n\n\n
  113. F McDonald, R I McLachlan, B E Moore, and G R W Quispel, Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations<\/a> J. Diff. Eq. Appl. 22(7) (2016), 913-940. <\/li>\n\n\n\n
  114. R I McLachlan, K Modin, and O Verdier, Symmetry reduction for central force problems<\/a> Eur. J. Phys. 37 (5) (2016) 055003. <\/li>\n\n\n\n
  115. L M Symes, R I McLachlan, and P B Blakie, Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation<\/a> Phys. Rev. E 93(5) (2016) 053309.<\/li>\n\n\n\n
  116. R I McLachlan, K Modin, and O Verdier, A minimal-variable symplectic integrator on spheres<\/a> Math. Comput. 86 (2017) 2325-2344. <\/li>\n\n\n\n
  117. V Grimm, RI McLachlan, D McLaren, GRW Quispel, CB Sch\u00f6nlieb, The use of discrete gradient methods for total variation type regularization problems in image processing<\/a>, Journal of Physics A: Mathematical and Theoretical 50 (29) 2017, 295201 <\/li>\n\n\n\n
  118. R I McLachlan, K Modin, H Munthe-Kaas, O Verdier, What are Butcher series, really? The story of rooted trees and numerical methods for evolution equations<\/a>, Asia-Pacific Mathematics Newsletter 7 (1) 2017, 1-11.<\/li>\n\n\n\n
  119. E Celledoni, RI McLachlan, DI McLaren, B Owren, GRW Quispel, Two classes of quadratic vector fields for which the Kahan discretization is integrable<\/a>, MI Lecture Notes of Institute of Mathematics for Industry, 74 (2017) 60-62.<\/li>\n\n\n\n
  120. V Grimm, R I McLachlan, DI McLaren, GRW Quispel, CB Schonlieb, Discrete gradient methods for solving variational image regularisation models<\/a>, Journal of Physics A: Mathematical and Theoretical 50 (29), 295201, 2017.<\/li>\n\n\n\n
  121. S R Marsland, R I McLachlan, C Tuffley, Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawat\u016b\u2013Whanganui region<\/a>, ANZIAM J 59 M63\u2013M125, 2017.<\/li>\n\n\n\n
  122. R I McLachlan, C Offen, Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci<\/a>, New Zealand Journal of Mathematics 48, 83-99 6, 2018.<\/li>\n\n\n\n
  123. R I McLachlan, C Offen, Bifurcation of solutions to Hamiltonian boundary value problems<\/a>, Nonlinearity 31 (6), 2895, 2018.<\/li>\n\n\n\n
  124. R I McLachlan, Men will stretch out their eyes: Or, What happened to Christopher Wren’s inaugural<\/a>, Bulletin of the Society for the History of Astronomy, 29, pp. 39-42, 2018.<\/li>\n\n\n\n
  125. R I McLachlan, C Offen, and B K Tapley, Symplectic integration of PDEs using Clebsch variables<\/a>, Journal of Computational Dynamics, 6, 111, 2019.<\/li>\n\n\n\n
  126. P H van der Kamp, E Celledoni, R I McLachlan, DI McLaren, B Owren, Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation<\/a>, Journal of Physics A: Mathematical and Theoretical 52 (4), 045204, 2019.<\/li>\n\n\n\n
  127. R I McLachlan, Perspectives on geometric numerical integration<\/a>, Journal of the Royal Society of New Zealand 49 (2), 114-125, 2019.<\/li>\n\n\n\n
  128. R I McLachlan, A Murua, The Lie algebra of classical mechanics<\/a>, J Comput Dyn 2019, 6(2): 345-360.<\/li>\n\n\n\n
  129. S Marsland, R I McLachlan, M C Wilkins, Parallelization, initialization, and boundary treatments for the diamond scheme<\/a>, Numerical Algorithms, 1-19, 2019.<\/li>\n\n\n\n
  130. R I McLachlan, C Offen, Symplectic integration of boundary value problems<\/a>, Numerical Algorithms 81 (4), 1219-1233, 2019.<\/li>\n\n\n\n
  131. SR Marsland, R I McLachlan, C Curry, Principal symmetric space analysis<\/a>, J Comput Dyn 2019, 6(2): 251-276.<\/li>\n\n\n\n
  132. J Benn, S Marsland, R I McLachlan, K Modin, O Verdier, Currents and finite elements as tools for shape space<\/a>, Journal of Mathematical Imaging and Vision 61 (8), 1197-1220, 2019.<\/li>\n\n\n\n
  133. RI McLachlan, Sea change: climate politics and New Zealand<\/a>, Journal of the Royal Society of New Zealand 49 (1), 64-69, 2019.<\/li>\n\n\n\n
  134. R I McLachlan, A Stern, Multisymplecticity of hybridizable discontinuous Galerkin methods<\/a>, Foundations of Computational Mathematics 20 (1), 35-69, 2020.<\/li>\n\n\n\n
  135. L M Kreusser, R I McLachlan, C Offen, Detection of high codimensional bifurcations in variational PDEs<\/a>, Nonlinearity 33 (5), 2335, 2020.<\/li>\n\n\n\n
  136. E Celledoni, M J Ehrhardt, C Etmann, R I McLachlan, B Owren, Structure-preserving deep learning<\/a>, European Journal of Applied Mathematics, 1-49, 2021.<\/li>\n\n\n\n
  137. S Marsland, R I McLachlan, M Y Tufail, Conformal image registration based on constrained optimization<\/a>, The ANZIAM Journal 62 (3), 235-255, 2020.<\/li>\n\n\n\n
  138. R I McLachlan, C Offen, Preservation of bifurcations of Hamiltonian boundary value problems under discretisation<\/a>, Foundations of Computational Mathematics 20 (6), 1363-1400, 2020.<\/li>\n\n\n\n
  139. S Marsland, R I McLachlan, R Zarre, Analysing `Simple’ Image Registrations<\/a>, Journal of Mathematical Imaging and Vision 63 (4), 528-540, 2021.<\/li>\n\n\n\n
  140. R I McLachlan, C Offen, Backward error analysis for variational discretisations of PDEs<\/a>, Journal of Geometric Mechanics 14 (3), 447, 2022.<\/li>\n\n\n\n
  141. R I McLachlan, Tuning symplectic integrators is easy and worthwhile<\/a>, Commun. Comput. Phys. 31(3), 987-996, 2022.<\/li>\n\n\n\n
  142. S S Muni, R I McLachlan, D J W Simpson, Unfolding globally resonant homoclinic tangencies<\/a>, Discrete and Continuous Dynamical Systems A, 2022. <\/li>\n\n\n\n
  143. R I McLachlan, C Offen, Backward error analysis for conjugate symplectic methods<\/a>, Journal of Geometric Mechanics, 2022.<\/li>\n\n\n\n
  144. M Hochbruck, C Lubich, R McLachlan, JM Sanz-Serna, Geometric Numerical Integration, Oberwolfach Reports 18 (2), 943-999, 2022.<\/a><\/li>\n\n\n\n
  145. D Hall, R McLachlan, Why emissions pricing can’t do it alone<\/a>, Policy Quarterly 18 (1), 3-13, 2022.<\/li>\n\n\n\n
  146. D Hall, R McLachlan, Why emissions pricing cannot do it alone<\/a> [longer version], 2022.<\/li>\n\n\n\n
  147. R I McLachlan, P Callister. Managing New Zealand\u2019s greenhouse gas emissions from aviation<\/a>. [longer version] Institute for Governance and Policy Studies, Working Paper 2022\/01. 2022.<\/li>\n\n\n\n
  148. R I McLachlan, D I McLaren, G R W Quispel. Birational maps from polarization and the preservation of measure and integrals<\/a>, Journal of Physics A: Mathematical and Theoretical 56 (36), 365202, 2023.<\/li>\n\n\n\n
  149. A Laurent, R I McLachlan, H Z Munthe-Kaas, O Verdier. The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators<\/a>. Forum of Mathematics, Sigma 11, e69, 2023.<\/li>\n\n\n\n
  150. P Callister, RI McLachlan, K Wild, A Woodward, An aviation emissions reduction plan for Aotearoa<\/a>, 2023.<\/li>\n\n\n\n
  151. P Callister, R McLachlan, Decarbonising Aotearoa New Zealand\u2019s aviation sector: hard to abate, but even harder to govern<\/a>, Policy Quarterly 19 (2), 9-18, 2023.<\/li>\n\n\n\n
  152. R McLachlan, Commentary: climate policy in Aotearoa New Zealand\u2013a backwards flip<\/a>, Policy Quarterly 19 (4), 106-111, 2023.<\/li>\n\n\n\n
  153. P Callister, R I McLachlan. Managing Aotearoa New Zealand’s greenhouse gas emissions from aviation<\/a>. Journal of the Royal Society of New Zealand 54 (4), 412-432, 2024.<\/li>\n\n\n\n
  154. I Ghosh, R I McLachlan, D J W Simpson. The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps<\/a>. Communications in Nonlinear Science and Numerical Simulation 134, 108025, 2024.<\/li>\n\n\n\n
  155. G Bogfjellmo, E Celledoni, R McLachlan, B Owren, G Quispel. Using aromas to search for preserved measures and integrals in Kahan\u2019s method<\/a>. Mathematics of Computation 93 (348), 1633-1653, 2024.<\/li>\n\n\n\n
  156. R I McLachlan, A Stern. Functional equivariance and conservation laws in numerical integration<\/a>. Foundations of Computational Mathematics 24 (1), 149-177, 2024.<\/li>\n\n\n\n
  157. P H van der Kamp, R I McLachlan, D I McLaren, G R W Quispel. Measure preservation and integrals for Lotka\u2013Volterra tree-systems and their Kahan discretisation<\/a>. J. Comput. Dyn. 11, 468–484, 2024.<\/li>\n\n\n\n
  158. R I McLachlan, The emissions impact of a shift to universal road user charging in New Zealand<\/a>. Technical report, 2025.<\/li>\n\n\n\n
  159. P Callister and R I McLachlan, Aviation emissions and New Zealand’s Aviation Action Pla<\/a>n<\/a>. Technical report, 2025.<\/li>\n\n\n\n
  160. R I McLachlan. Runge\u2013Kutta methods determined from extended phase space methods for Hamiltonian systems<\/a>. Numerical Algorithms, 100:983\u2013993, 2025.<\/li>\n\n\n\n
  161. I Ghosh, RI McLachlan, DJW Simpson. Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps<\/a>. Journal of Nonlinear Science 35 (1), 16, 2025.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":294,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/pages\/5","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/users\/294"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/comments?post=5"}],"version-history":[{"count":10,"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/pages\/5\/revisions"}],"predecessor-version":[{"id":214,"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/pages\/5\/revisions\/214"}],"wp:attachment":[{"href":"https:\/\/sites.massey.ac.nz\/robertmclachlan\/wp-json\/wp\/v2\/media?parent=5"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}