[1] Robert I McLachlan and GRW Quispel. Discrete gradient methods have an energy conservation law. Disc. Cont. Dyn. S. A, 34(3):1099-1104, 2014. [ bib | .pdf ]
[2] Elena Celledoni, Robert I McLachlan, David I McLaren, Brynjulf Owren, and GRW Quispel. Integrability properties of Kahan's method. arXiv:1405.3740, 2014. [ bib | http ]
[3] Stephen Marsland, Robert I McLachlan, Klas Modin, and Matthew Perlmutter. On conformal variational problems and free boundary continua. Journal of Physics A: Mathematical and Theoretical, 47(14):145204, 2014. [ bib | .pdf ]
[4] Robert I McLachlan, Klas Modin, and Olivier Verdier. Discrete time Hamiltonian spin systems. arXiv:1402.3334, 2014. [ bib | .pdf ]
[5] Robert I McLachlan, Klas Modin, and Olivier Verdier. Symplectic integrators for spin systems. arXiv:1402.4114, 2014. [ bib | http ]
[6] Robert I McLachlan, Klas Modin, and Olivier Verdier. Collective symplectic integrators. Nonlinearity, 27:1525-1542, 2014. [ bib | http ]
[7] Robert McLachlan, Klas Modin, and Olivier Verdier. Collective Lie-Poisson integrators on R^3. IMA J Numer. Anal., 2014. [ bib | http ]
[8] Robert I McLachlan and Ari Stern. Modified trigonometric integrators. SIAM J. Numer. Anal., 2014. [ bib | http ]
[9] Ayesha Hakim, Stephen Marsland, and Hans W Guesgen. Computational analysis of emotion dynamics. In Affective Computing and Intelligent Interaction (ACII), 2013 Humaine Association Conference on, pages 185-190. IEEE, 2013. [ bib | http ]
[10] Stephen Marsland, Robert I McLachlan, Klas Modin, and Matthew Perlmutter. Geodesic warps by conformal mappings. International Journal of Computer Vision, 105(2):144-154, 2013. [ bib | .pdf ]
[11] Robert I McLachlan, Klas Modin, Olivier Verdier, and Matt Wilkins. Symplectic integrators for index one constraints. SIAM Journal on Scientific Computing, 35(5):A2150-A2162, 2013. [ bib | .pdf ]
[12] Robert I McLachlan, Klas Modin, Olivier Verdier, and Matt Wilkins. Geometric generalisations of SHAKE and RATTLE. Foundations of Computational Mathematics, pages 1-32, 2013. [ bib | .pdf ]
[13] Elena Celledoni, Robert I McLachlan, Brynjulf Owren, and GRW Quispel. Geometric properties of Kahan's method. Journal of Physics A: Mathematical and Theoretical, 46(2):025201, 2013. [ bib | .pdf ]
[14] Carole J Twining and Stephen Marsland. Discrete differential geometry: The nonplanar quadrilateral mesh. Physical Review E, 85(6):066708, 2012. [ bib | http ]
[15] Elena Celledoni, V Grimm, Robert I McLachlan, DI McLaren, D O'Neale, Brynjulf Owren, and GRW Quispel. Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Journal of Computational Physics, 231(20):6770-6789, 2012. [ bib | .pdf ]
[16] Robert I McLachlan and Xing You Zhang. Asymptotic profiles for modified Camassa-Holm equations. SIAM J. Appl. Dyn. Sys., 10:452-468, 2011. [ bib | .pdf ]
[17] K. Modin, M. Perlmutter, S. Marsland, and R. I. McLachlan. On Euler-Arnold equations and totally geodesic subgroups. Journal of Geometry and Physics, 61:1446-1461, 2011. [ bib ]
[18] Stephen Marsland, Robert I McLachlan, Klas Modin, and Matt Perlmutter. On a geodesic equation for planar conformal template matching. In 3rd Workshop on Mathematical Foundations of Computational Anatomy, pages 52-63, 2011. [ bib ]
[19] Klas Modin and Gustaf Soderlind. Geometric integration of Hamiltonian systems perturbed by Rayleigh damping. BIT Numer Math, 51:977-1007, 2011. [ bib ]
[20] K. Modin, M. Perlmutter, S. Marsland, and R. I. McLachlan. Geodesics on Lie groups: Euler equations and totally geodesic subgroups. Technical report, Res. Lett. Inf. Math. Sci. (Massey University), vol. 14, pp. 79-106, 2011. [ bib | http ]
[21] RI McLachlan, Y Sun, and PSP Tse. Linear stability of partitioned Runge-Kutta methods. SIAM J Numer Anal, 49:232-263, 2011. [ bib ]
[22] Elena Celledoni, Robert I McLachlan, Brynjulf Owren, and GWR Quispel. Energy-preserving integrators and the structure of B-series. Foundations Comput Math, 10:673-693, 2010. [ bib ]
[23] Elena Celledoni, Robert I McLachlan, Brynjulf Owren, and GWR Quispel. On conjugate B-series and their geometric structure. J Numer Anal Indust Appl Math (JNAIAM), 5:85-94, 2010. [ bib ]
[24] DRJ O'Neale and RI McLachlan. Preservation and destruction of periodic orbits by symplectic integrators. Numerical Algorithms, 53:343-362, 2010. [ bib ]
[25] AJ Elvin, CR Laing, RI McLachlan, and MG Roberts. Exploiting the Hamiltonian structure of a neural field model. Physica D, 239:537-546, 2010. [ bib ]
[26] Matthew Liu, Ken Hawick, Stephen Marsland, and Rui Jiang. Spontaneous symmetry breaking in asymmetric exclusion process with constrained boundaries and site sharing: A Monte Carlo study. Physica A: Statistical Mechanics and its Applications, 389(18):3870-3875, 2010. [ bib ]
[27] Matthew Liu, Ken Hawick, and Stephen Marsland. Asymmetric exclusion processes with site sharing in a one-channel transport system. Physics Letters A, 374(4):516-521, 2010. [ bib ]
[28] DRJ O'Neale and RI McLachlan. Preservation and destruction of periodic orbits by symplectic integrators. Numerical Algorithms, 53:343-362, 2010. [ bib ]
[29] Elena Celledoni, Robert I McLachlan, Brynjulf Owren, and GWR Quispel. Structure of B-series for some classes of geometric integrators. In AIP Conference Proceedings 1168, pages 739-742, 2009. [ bib ]
[30] Klas Modin. Time-transformation and reversibility of Nambu-Poisson systems. J. Gen. Lie Theory Appl., 3(1):39-52, 2009. [ bib ]
[31] DRJ O'Neale and RI McLachlan. Reconsidering trigonometric integrators. ANZIAM Journal, 50:320-332, 2009. [ bib ]
[32] E Hairer, RI McLachlan, and RD Skeel. On energy behaviour of the modified Takahashi-Imada method. Mathematical Modelling and Numerical Analysis, 43:631-644, 2009. [ bib ]
[33] E Celledoni, RI McLachlan, DI McLaren, B Owren, GRW Quispel, and W Wright. Energy-preserving Runge-Kutta methods. Mathematical Modelling and Numerical Analysis, 43:645-649, 2009. [ bib ]
[34] RI McLachlan, GWR Quispel, and PSP Tse. Linearization-preserving self-adjoint and symplectic integrators. BIT, 49(1):177-197, 2009. [ bib ]
[35] RI McLachlan. The structure of a set of vector fields on Poisson manifolds. J. Phys. A: Math. Theor., 42:142001, 2009. [ bib ]
[36] McLachlan RI and X Zhang. Well-posedness of modified Camassa-Holm equations. J. Differential Equations, 246:3241-3259, 2009. [ bib ]
[37] Klas Modin. On explicit adaptive symplectic integration of separable Hamiltonian systems. J. Mult. Body Mech., 222(4):1464-1493, 2008. [ bib ]
[38] Elena Celledoni, Robert I McLachlan, DI McLaren, Brynjulf Owren, GWR Quispel, and W Wright. Energy-preserving methods and B-series. In T Kvamsdal, KM Mathisen, and B Pettersen, editors, Proc. 21st Nordic Seminar on Computational Mathematics, 2008. [ bib ]
[39] BN Ryland and RI McLachlan. On multisymplecticity of partitioned Runge-Kutta methods. SIAM J. Sci. Comput., 30(3):1318-1340, 2008. [ bib ]
[40] E Hairer, RI McLachlan, and A Razakarivony. Achieving Brouwer's law with implicit Runge-Kutta methods. BIT, 48(2):231-244, 2008. [ bib ]
[41] RI McLachlan, HZ Munthe-Kaas, GWR Quispel, and A Zanna. Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. Foundations Comput. Math., 8:335-355, 2008. [ bib ]
[42] Matthew Perlmutter and Miguel Rodriguez-Olmos. On singular Poisson-Sternberg spaces, 2008. [ bib | http ]
[43] Stephen Marsland, Carole Twining, and Chris Taylor. A minimum description length objective function for groupwise non-rigid image registration. Image and Vision Computing, 26(3):333-346, 2008. [ bib | .pdf ]
[44] Carole Twining and Stephen Marsland. Constructing an atlas for the diffeomorphism group of a compact manifold with boundary, with application to the analysis of image registrations. Journal of Computational and Applied Mathematics, 222:411-428, 2008. [ bib | .pdf ]
[45] M. Perlmutter, M. Rodriguez-Olmos, and M.E. Sousa-Dias. The symplectic normal space of a cotangent-lifted action. Differential Geometry and its Applications, 26(3):277-297, 2008. [ bib ]
[46] M. Perlmutter, M. Rodriguez-Olmos, and M.E. Sousa-Dias. On the geometry of reduced cotangent bundles at zero momentum. Journal of Geometry and Physics, 57(2):571-596, 2008. [ bib ]
[47] Robert I McLachlan. A new implementation of symplectic Runge-Kutta methods. SIAM J Sci Comput, 29(4):1637-1649, 2007. [ bib ]
[48] B.N. Ryland, R.I. McLachlan, and J. Frank. On multisymplecticity of partitioned Runge-Kutta and splitting methods. Int J Comput Math, 84(6):847-869, 2007. [ bib ]
[49] Robert I McLachlan and Stephen Marsland. N-particle dynamics of the Euler equations for planar diffeomorphisms. Dynamical Systems, 22(3), 2007. [ bib | .pdf ]
[50] Robert I McLachlan and Stephen Marsland. Discrete mechanics and optimal control for image registration. ANZIAM Journal, 48:C1-C16, 2007. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/82 [April 23, 2007]. [ bib | http ]
[51] Stephen Marsland and Robert I McLachlan. A Hamiltonian particle method for diffeomorphic image registration. In Proceedings of Information Processing in Medical Images, volume 4548 of Lecture Notes in Computer Science, pages 396-407. Springer, 2007. [ bib | .pdf ]
[52] K Modin and C Fuhrer. Time-step adaptivity in variational integrators with application to contact problems. ZAMM Z. Angew. Math. Mech., 86(10):785-794, 2006. [ bib ]
[53] I.G. Mason, R.I. McLachlan, and D. Gerard. A double exponential model for biochemical oxygen demand. Bioresource Technology, 97(2):273-282, 2006. [ bib ]
[54] R.I. McLachlan and G.W.R. Quispel. Geometric integrators for ODEs. J. Phys. A, 39(19):5251-5286, 2006. [ bib | .pdf ]
[55] R.I. McLachlan and D.R. O'Neale. Geometric integration for a two-spin system. J. Phys. A: Math. Gen., 39:L447-L452, 2006. [ bib | .pdf ]
[56] R.I. McLachlan and M. Perlmutter. Integrators for nonholonomic mechanical systems. J Nonlinear Sci, 16(4):283-328, 2006. [ bib | .pdf ]
[57] R.I. McLachlan. Integration and applications of generalized euler equations, 2006. [ bib ]
[58] Robert I McLachlan and Stephen Marsland. The Kelvin-Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms. SIAM Journal on Applied Dynamical Systems, 5(4):726-758, 2006. Animations of the systems in this paper are available at http://www-ist.massey.ac.nz/smarsland/KelvinHelmholtz.html. [ bib | DOI | .pdf ]
[59] Carole Twining, Tim Cootes, Stephen Marsland, Vladimir Petrovic, Roy Schestowitz, and Chris Taylor. Information-theoretic unification of groupwise non-rigid registration and model building. In Proceedings of Medical Image Understanding and Analysis (MIUA), volume 2, pages 226-230, 2006. [ bib ]
[60] Robert I McLachlan and Stephen Marsland. Discrete mechanics and optimal control for image registration. In Computational Techniques and Applications Conference (CTAC), 2006. [ bib ]
[61] Anna Mills, Stephen Marsland, and Tony Shardlow. Computing the geodesic interpolating spline. In JPW Pluim, B Likar, and FA Gerritsen, editors, Biomedical Image Registration, Third International Workshop (WBIR), number 4057 in Lecture Notes in Computer Science, pages 169-177, Berlin, 2006. Springer. [ bib | .pdf ]
[62] Xing-you Zhang and Yong Huang. Homogenization for degenerate quasilinear parabolic equations of second order. Acta Mathematicae Applicatae Sinica, 21(1):93-100, 2005. [ bib ]
[63] Tunhua Zhou and Xingyou Zhang. Stability of C^0 semigroups which possess global attractors. Dynamical Systems, 20(2):233-236, 2005. [ bib ]
[64] Chuandong Li, Xiaofeng Liao, and Xingyou Zhang. Impulsive synchronization of chaotic systems. Chaos, 15, 2005. [ bib ]
[65] Carole Twining, Tim Cootes, Stephen Marsland, Roy Schestowitz, Vladimir Petrovic, and Chris Taylor. A unified information-theoretic approach to groupwise non-rigid registration and model building. In Gary Christensen and Milan Sonka, editors, 19th International Conference on Information Processing in Medical Images (IPMI'05), volume 3565 of Lecture Notes in Computer Science, pages 1-14. Springer, 2005. [ bib ]
[66] R.I. McLachlan and A. Zanna. The discrete Moser-Veselov algorithm for the free rigid body, revisited. Foundations of Comput. Math., 5:87-123, 2005. [ bib | .pdf ]
[67] U. Ascher and R.I. McLachlan. On symplectic and multisymplectic schemes for the KdV equations. J. Sci. Comput., 25(1):83-104, 2005. [ bib | .pdf ]
[68] Stephen Marsland and Carole Twining. Constructing diffeomorphic representations for the groupwise analysis of non-rigid registrations of medical images. IEEE Transactions on Medical Imaging, 23(8):1006-1020, 2004. [ bib | .pdf ]
[69] Stephen Marsland and Carole Twining. A minimum description length objective function for groupwise non-rigid image registration. In Image and Vision Computing, New Zealand, pages 203-208, 2004. [ bib | .pdf ]
[70] Carole Twining, Stephen Marsland, and Chris Taylor. Groupwise non-rigid registration: The minimum description length approach. In British Machine Vision Conference, 2004. [ bib | .pdf ]
[71] Carole Twining, Stephen Marsland, and Chris Taylor. Groupwise non-rigid registration of medical images: The minimum description length approach. In Medical Image Analysis and Understanding, pages 81-84, 2004. [ bib | .pdf ]
[72] Stephen Marsland and Iain Buchan. Clinical quality needs complex adaptive systems and machine learning. In Proceedings of the International Conference on Medical Informatics, pages 644-647, 2004. [ bib | .pdf ]
[73] Carole Twining and Stephen Marsland. A unified information-theoretic approach to the correspondence problem in image registration. In International Conference on Pattern Recognition, volume 3, pages 704-709, 2004. [ bib | .pdf ]
[74] Tim Cootes, Stephen Marsland, Carole Twining, Kate Smith, and Chris Taylor. Groupwise diffeomorphic non-rigid registration for automatic model building. In Proceedings of the European Conference on Computer Vision, volume 3024 of Lecture Notes in Computer Science, pages 316-327. Springer, 2004. [ bib ]
[75] U. Ascher and R.I. McLachlan. Multisymplectic box schemes and the Korteweg-de Vries equation. Appl. Numer. Math., 48:255-269, 2004. [ bib | .pdf ]
[76] R.I. McLachlan and Quispel. G.W.R. Explicit geometric integration of polynomial vector fields. BIT, 44:515-538, 2004. [ bib | .pdf ]
[77] R.I. McLachlan, M. Perlmutter, and G.W.R. Quispel. On the nonlinear stability of symplectic integrators. BIT, 44:99-117, 2004. [ bib | .pdf ]
[78] R.I. McLachlan and M. Perlmutter. Energy drift in reversible time integration. J. Phys. A, 37(45):L593-L598, 2004. [ bib | .pdf ]

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