On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods. - Robert I. McLachlan (SIAM J. Sci. Comput., 1995)

Families of High-Order Composition Methods. - Robert I. McLachlan (Numer. Algorithms, 2002)

Lie group foliations: dynamical systems and integrators. - Robert I. McLachlan; Matthew Perlmutter; G. R. W. Quispel (Future Gener. Comput. Syst., 2003)

The Discrete Moser-Veselov Algorithm for the Free Rigid Body, Revisited. - Robert I. McLachlan; Antonella Zanna (Found. Comput. Math., 2005)

On Symplectic and Multisymplectic Schemes for the KdV Equation. - Uri M. Ascher; Robert I. McLachlan (J. Sci. Comput., 2005)

Integrators for Nonholonomic Mechanical Systems. - Robert I. McLachlan; Matthew Perlmutter (J. Nonlinear Sci., 2006)

The Kelvin-Helmholtz Instability of Momentum Sheets in the Euler Equations for Planar Diffeomorphisms. - Robert I. McLachlan; Stephen R. Marsland (SIAM J. Appl. Dyn. Syst., 2006)

A Hamiltonian Particle Method for Diffeomorphic Image Registration. - Stephen R. Marsland; Robert I. McLachlan (IPMI, 2007)

On the multisymplecticity of partitioned Runge-Kutta and splitting methods. - Brett N. Ryland; Robert I. McLachlan; Jason Frank (Int. J. Comput. Math., 2007)

A New Implementation of Symplectic Runge-Kutta Methods. - Robert I. McLachlan (SIAM J. Sci. Comput., 2007)

Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields. - Robert I. McLachlan; Hans Z. Munthe-Kaas; G. R. W. Quispel; Antonella Zanna (Found. Comput. Math., 2008)

On Multisymplecticity of Partitioned Runge-Kutta Methods. - Brett N. Ryland; Robert I. McLachlan (SIAM J. Sci. Comput., 2008)

Energy-Preserving Integrators and the Structure of B-series. - Elena Celledoni; Robert I. McLachlan; Brynjulf Owren; G. R. W. Quispel (Found. Comput. Math., 2010)

Preservation and destruction of periodic orbits by symplectic integrators. - Robert I. McLachlan; Dion R. J. O'Neale (Numer. Algorithms, 2010)

Asymptotic Blowup Profiles for Modified Camassa-Holm Equations. - Robert I. McLachlan; Xingyou Zhang (SIAM J. Appl. Dyn. Syst., 2011)

Linear Stability of Partitioned Runge-Kutta Methods. - Robert I. McLachlan; Yajuan Sun; P. S. P. Tse (SIAM J. Numer. Anal., 2011)

Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method. - Elena Celledoni; Volker Grimm; Robert I. McLachlan; David I. McLaren; Dion R. J. O'Neale; Brynjulf Owren; G. R. W. Quispel (J. Comput. Phys., 2012)

Geodesic Warps by Conformal Mappings. - Stephen R. Marsland; Robert I. McLachlan; Klas Modin; Matthew Perlmutter (Int. J. Comput. Vis., 2013)

Symplectic Integrators for Index 1 Constraints. - Robert I. McLachlan; Klas Modin; Olivier Verdier; Matt Wilkins (SIAM J. Sci. Comput., 2013)

Geometric Generalisations of shake and rattle. - Robert I. McLachlan; Klas Modin; Olivier Verdier; Matt Wilkins (Found. Comput. Math., 2014)

Modified Trigonometric Integrators. - Robert I. McLachlan; Ari Stern (SIAM J. Numer. Anal., 2014)

High Order Multisymplectic Runge-Kutta Methods. - Robert I. McLachlan; Brett N. Ryland; Yajuan Sun (SIAM J. Sci. Comput., 2014)

The Multisymplectic Diamond Scheme. - Robert I. McLachlan; Matt Wilkins (SIAM J. Sci. Comput., 2015)

Möbius invariants of shapes and images. - Stephen Marsland; Robert I. McLachlan (CoRR, 2016)

Geometry of Discrete-Time Spin Systems. - Robert I. McLachlan; Klas Modin; Olivier Verdier (J. Nonlinear Sci., 2016)

B-series methods are exactly the affine equivariant methods. - Robert I. McLachlan; Klas Modin; Hans Z. Munthe-Kaas; Olivier Verdier (Numerische Mathematik, 2016)

A minimal-variable symplectic integrator on spheres. - Robert I. McLachlan; Klas Modin; Olivier Verdier (Math. Comput., 2017)

Currents and Finite Elements as Tools for Shape Space. - James Benn; Stephen Marsland; Robert I. McLachlan; Klas Modin; Olivier Verdier (J. Math. Imaging Vis., 2019)

Symplectic integration of boundary value problems. - Robert I. McLachlan; Christian Offen (Numer. Algorithms, 2019)

Structure preserving deep learning. - Elena Celledoni; Matthias J. Ehrhardt; Christian Etmann; Robert I. McLachlan; Brynjulf Owren; Carola-Bibiane Schönlieb; Ferdia Sherry (CoRR, 2020)

Backward error analysis for variational discretisations of partial differential equations. - Robert I. McLachlan; Christian Offen (CoRR, 2020)

Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation. - Robert I. McLachlan; Christian Offen (Found. Comput. Math., 2020)

Multisymplecticity of Hybridizable Discontinuous Galerkin Methods. - Robert I. McLachlan; Ari Stern (Found. Comput. Math., 2020)

Parallelization, initialization, and boundary treatments for the diamond scheme. - Stephen Marsland; Robert I. McLachlan; Matt Wilkins (Numer. Algorithms, 2020)

Tuning symplectic integrators is easy and worthwhile. - Robert I. McLachlan (CoRR, 2021)

Analysing 'Simple' Image Registrations. - Stephen Marsland; Robert I. McLachlan; Raziyeh Zarre (J. Math. Imaging Vis., 2021)

Backward error analysis for conjugate symplectic methods. - Robert I. McLachlan; Christian Offen (CoRR, 2022)

The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators. - Adrien Laurent; Robert I. McLachlan; Hans Z. Munthe-Kaas; Olivier Verdier (CoRR, 2023)

Birational maps from polarization and the preservation of measure and integrals. - Robert I. McLachlan; David I. McLaren; G. R. W. Quispel (CoRR, 2023)

Runge-Kutta methods determined from extended phase space methods for Hamiltonian systems. - Robert I. McLachlan (CoRR, 2023)

Measure preservation and integrals for Lotka-Volterra T-systems and their Kahan discretisation. - Peter H. van der Kamp; Robert I. McLachlan; David I. McLaren; G. R. W. Quispel (CoRR, 2023)

Using aromas to search for preserved measures and integrals in Kahan's method. - Geir Bogfjellmo; Elena Celledoni; Robert I. McLachlan; Brynjulf Owren; Reinout Quispel (Math. Comput., 2023)

The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps. - Indranil Ghosh; Robert I. McLachlan; David J. W. Simpson (Commun. Nonlinear Sci. Numer. Simul., 2024)

Functional Equivariance and Conservation Laws in Numerical Integration. - Robert I. McLachlan; Ari Stern (Found. Comput. Math., 2024)

Robust Chaos in Orientation-Reversing and Non-Invertible Two-Dimensional Piecewise-Linear Maps. - Indranil Ghosh; Robert I. McLachlan; David J. W. Simpson (J. Nonlinear Sci., 2025)