Edit Profile (opens in new tab) McLachlan, Robert I. Compute Distance To: Compute Author ID: mclachlan.robert-i Published as: McLachlan, Robert I.; McLachlan, R. I.; McLachlan, Robert; Mclachlan, Robert I.; Mclachlan, R. I.; McLachlan, R. more...less Documents Indexed: 106 Publications since 1991 1 Contribution as Editor Co-Authors: 55 Co-Authors with 91 Joint Publications 772 Co-Co-Authors all top 5 Co-Authors 16 single-authored 24 Quispel, Gilles Reinout Willem 12 Marsland, Stephen R. 12 Modin, Klas 11 Celledoni, Elena 10 Owren, Brynjulf 9 Verdier, Olivier 7 Perlmutter, Matthew 6 McLaren, David I. 6 Offen, Christian 4 O’Neale, Dion R. J. 4 Robidoux, Nicolas 4 Ryland, Brett N. 4 Wilkins, Matthew C. 3 Atela, Pau 3 Zanna, Antonella 3 Zeitlin, Vladimir 2 Ascher, Uri M. 2 Grimm, Volker 2 Hairer, Ernst 2 Munthe-Kaas, Hans Z. 2 Quispel, Reinout 2 Schönlieb, Carola-Bibiane 2 Scovel, Clint 2 Stern, Ari 2 Sun, Yajuan 2 Tse, P. S. P. 2 Zhang, Xingyou 1 Benn, James 1 Curry, Charles 1 Ehrhardt, Matthias Joachim 1 Elvin, A. J. 1 Etmann, Christian 1 Frank, Jason 1 Gray, Stephen K. 1 Iserles, Arieh 1 Kitson, Adrian 1 Kreusser, Lisa Maria 1 Laing, Carlo R. 1 McDonald, Fleur 1 Moore, Brian E. 1 Muni, Sishu Shankar 1 Murua, Ander 1 Razakarivony, A. 1 Roberts, Michael George 1 Segur, Harvey 1 Sherry, Ferdia 1 Simpson, David John Warwick 1 Skeel, Robert D. 1 Szunyogh, Istvan 1 Tapley, Benjamin K. 1 Tufail, M. Y. 1 Turner, G. S. 1 van der Kamp, Peter H. 1 Wright, William M. 1 Zarre, Raziyeh all top 5 Serials 6 SIAM Journal on Scientific Computing 6 Foundations of Computational Mathematics 6 Journal of Physics A: Mathematical and Theoretical 5 Nonlinearity 5 BIT 4 Applied Numerical Mathematics 4 Numerical Algorithms 4 Journal of Computational Dynamics 3 Physics Letters. A 3 SIAM Journal on Numerical Analysis 3 Journal of Physics A: Mathematical and General 3 Journal of Nonlinear Science 3 The ANZIAM Journal 2 IMA Journal of Numerical Analysis 2 Journal of Geometry and Physics 2 Numerische Mathematik 2 Physica D 2 European Journal of Applied Mathematics 2 New Zealand Journal of Mathematics 2 Journal of Mathematical Imaging and Vision 2 Discrete and Continuous Dynamical Systems 2 Physical Review Letters 2 SIAM Journal on Applied Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Computers & Mathematics with Applications 1 European Journal of Physics 1 Journal of Computational Physics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Physics 1 Physics of Fluids, A 1 Mathematics of Computation 1 The Mathematical Intelligencer 1 Journal of Differential Equations 1 Journal of Scientific Computing 1 International Journal of Computer Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Physics of Fluids 1 International Journal of Computer Vision 1 Journal of Difference Equations and Applications 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Dynamical Systems 1 Acta Numerica 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Communications in Computational Physics 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 68 Numerical analysis (65-XX) 63 Dynamical systems and ergodic theory (37-XX) 23 Mechanics of particles and systems (70-XX) 21 Partial differential equations (35-XX) 14 Ordinary differential equations (34-XX) 9 Differential geometry (53-XX) 6 Fluid mechanics (76-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Computer science (68-XX) 3 Nonassociative rings and algebras (17-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Group theory and generalizations (20-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 93 Publications have been cited 1,665 times in 1,044 Documents Cited by ▼ Year ▼ Splitting methods. Zbl 1105.65341McLachlan, Robert I.; Quispel, G. Reinout W. 222 2002 Geometric integration using discrete gradients. Zbl 0933.65143McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas 177 1999 Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Zbl 1284.65184Celledoni, E.; Grimm, V.; McLachlan, R. I.; McLaren, D. I.; O’Neale, D.; Owren, B.; Quispel, G. R. W. 115 2012 On the numerical integration of ordinary differential equations by symmetric composition methods. Zbl 0821.65048McLachlan, Robert I. 100 1995 Symplectic integration of Hamiltonian wave equations. Zbl 0831.65099McLachlan, Robert 69 1994 Multisymplectic box schemes and the Korteweg-de Vries equation. Zbl 1038.65138Ascher, Uri M.; McLachlan, Robert I. 64 2004 The accuracy of symplectic integrators. Zbl 0747.58032McLachlan, Robert I.; Atela, Pau 63 1992 Energy-preserving Runge-Kutta methods. Zbl 1169.65348Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. Reinout W.; Wright, William M. 47 2009 Geometric numerical integration of differential equations. Zbl 1092.65055McLachlan, Robert; Quispel, Reinout 46 2006 On symplectic and multisymplectic schemes for the KdV equation. Zbl 1203.65277Ascher, U. M.; Mclachlan, R. I. 40 2005 Explicit Lie-Poisson integration and the Euler equations. Zbl 0972.65509McLachlan, Robert I. 37 1993 Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals. Zbl 1042.37522McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas 32 1998 Conformal Hamiltonian systems. Zbl 1005.53058McLachlan, Robert; Perlmutter, Matthew 31 2001 Integrators for nonholonomic mechanical systems. Zbl 1104.37043McLachlan, R.; Perlmutter, M. 31 2006 Geometric properties of Kahan’s method. Zbl 1278.65192Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W. 26 2012 Energy-preserving integrators and the structure of B-series. Zbl 1205.65325Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W. 25 2010 Composition methods in the presence of small parameters. Zbl 0832.65071McLachlan, Robert I. 24 1995 A survey of open problems in symplectic integration. Zbl 0871.65058McLachlan, Robert I.; Scovel, Clint 23 1996 Numerical integrators that preserve symmetries and reversing symmetries. Zbl 0912.34015McLachlan, R. I.; Quispel, G. R. W.; Turner, G. S. 21 1998 Well-posedness of modified Camassa-Holm equations. Zbl 1203.35079McLachlan, Robert; Zhang, Xingyou 21 2009 Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058Hairer, E.; McLachlan, R. I.; Razakarivony, A. 20 2008 Discrete gradient methods have an energy conservation law. Zbl 1282.65112McLachlan, Robert I.; Quispel, G. R. W. 19 2014 What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration. Zbl 0994.65138McLachlan, Robert I.; Quispel, G. R. W. 17 2001 On the multisymplecticity of partitioned Runge-Kutta and splitting methods. Zbl 1125.65115Ryland, Brett N.; McLachlan, Robert I.; Frank, Jason 17 2007 Integrability properties of Kahan’s method. Zbl 1336.37045Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W. 17 2014 Equivariant constrained symplectic integration. Zbl 0836.58017McLachlan, R. I.; Scovel, C. 16 1995 Six lectures on the geometric integration of ODEs. Zbl 0978.65056McLachlan, Robert; Quispel, Reinout 16 2001 High order multisymplectic Runge-Kutta methods. Zbl 1310.37044McLachlan, Robert I.; Ryland, Brett N.; Sun, Yajuan 13 2014 B-series methods are exactly the affine equivariant methods. Zbl 1364.65145McLachlan, Robert I.; Modin, Klas; Munthe-Kaas, Hans; Verdier, Olivier 12 2016 The discrete Moser-Veselov algorithm for the free rigid body, revisited. Zbl 1123.70012McLachlan, Robert I.; Zanna, Antonella 11 2005 Linearization-preserving self-adjoint and symplectic integrators. Zbl 1162.65411McLachlan, R. I.; Quispel, G. R. W.; Tse, P. S. P. 11 2009 Modified trigonometric integrators. Zbl 1320.65194McLachlan, Robert I.; Stern, Ari 11 2014 On Euler-Arnold equations and totally geodesic subgroups. Zbl 1221.53118Modin, Klas; Perlmutter, Matthew; Marsland, Stephen; McLachlan, Robert 11 2011 Exploiting the Hamiltonian structure of a neural field model. Zbl 1203.37034Elvin, A. J.; Laing, C. R.; McLachlan, R. I.; Roberts, M. G. 10 2010 Families of high-order composition methods. Zbl 1016.65044McLachlan, Robert I. 10 2002 Global behavior of the charged isosceles three-body problem. Zbl 0900.70157Atela, Pau; McLachlan, Robert I. 10 1994 On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D. 10 2009 Discretization of polynomial vector fields by polarization. Zbl 1372.65201Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W. 9 2015 A minimal-variable symplectic integrator on spheres. Zbl 1364.37166McLachlan, Robert; Modin, Klas; Verdier, Olivier 9 2017 Collective symplectic integrators. Zbl 1333.65139McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 8 2014 Skew-adjoint finite difference methods on nonuniform grids. Zbl 1073.65084Kitson, Adrian; McLachlan, Robert I.; Robidoux, Nicolas 8 2003 Approximately preserving symmetries in the numerical integration of ordinary differential equations. Zbl 0939.65139Iserles, Arieh; McLachlan, Robert; Zanna, Antonella 7 1999 Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. Zbl 1147.65053McLachlan, R. I.; Munthe-Kaas, H. Z.; Quispel, G. R. W.; Zanna, A. 7 2008 On multisymplecticity of partitioned Runge-Kutta methods. Zbl 1172.37030Ryland, Brett N.; McLachlan, Robert I. 7 2008 Geometric generalisations of SHAKE and RATTLE. Zbl 1347.37131McLachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt 7 2014 Discrete gradient methods for solving variational image regularisation models. Zbl 1371.94146Grimm, V.; McLachlan, Robert I.; McLaren, David I.; Quispel, G. R. W.; Schönlieb, C.-B. 7 2017 Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation. Zbl 1422.70012van der Kamp, Peter H.; Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W. 7 2019 Linear stability of partitioned Runge-Kutta methods. Zbl 1228.65124McLachlan, R. I.; Sun, Y.; Tse, P. S. P. 7 2011 The multisymplectic diamond scheme. Zbl 1334.37095McLachlan, R. I.; Wilkins, M. C. 6 2015 Antisymmetry, pseudospectral methods, and conservative PDEs. Zbl 0963.65105McLachlan, Robert I.; Robidoux, Nicolas 6 2000 A gallery of constant-negative-curvature surfaces. Zbl 0812.53003McLachlan, Robert 6 1994 Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation. Zbl 0888.65095McLachlan, Robert I.; Gray, Stephen K. 6 1997 Generating functions for dynamical systems with symmetries, integrals, and differential invariants. Zbl 1194.37089Mclachlan, Robert I.; Quispel, G. R. W. 6 1998 Energy drift in reversible time integration. Zbl 1064.37063McLachlan, R. I.; Perlmutter, M. 6 2004 Collective Lie-Poisson integrators on \(\mathbb{R}^{3}\). Zbl 1318.65079McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 5 2015 Geometric integration of conservative polynomial ODEs. Zbl 1021.65064McLachlan, Robert I.; Quispel, G. R. W. 5 2003 \(N\)-particle dynamics of the Euler equations for planar diffeomorphisms. Zbl 1149.37038McLachlan, Robert I.; Marsland, Stephen 5 2007 More on symplectic correctors. Zbl 0872.65060McLachlan, Robert I. 5 1996 A new implementation of symplectic Runge-Kutta methods. Zbl 1145.65111McLachlan, Robert I. 5 2007 Explicit geometric integration of polynomial vector fields. Zbl 1066.65150McLachlan, Robert I.; Quispel, G. Reinout W. 5 2004 Spatial discretization of partial differential equations with integrals. Zbl 1080.65076McLachlan, Robert I. 5 2003 Bifurcation of solutions to Hamiltonian boundary value problems. Zbl 1402.37067Mclachlan, R. I.; Offen, C. 5 2018 A note on the motion of surfaces. Zbl 0961.53500McLachlan, Robert I.; Segur, Harvey 4 1994 Area preservation in computational fluid dynamics. Zbl 0966.76073McLachlan, Robert I. 4 1999 Comment on “Poisson schemes for Hamiltonian systems on Poisson manifolds”. Zbl 0821.58020McLachlan, R. 4 1995 Multisymplecticity of hybridizable discontinuous Galerkin methods. Zbl 1472.65147Mclachlan, Robert I.; Stern, Ari 4 2020 On the nonlinear stability of symplectic integrators. Zbl 1070.65130McLachlan, Robert I.; Perlmutter, Matthew; Quispel, G. R. W. 3 2004 The boundary layer on a finite flat plate. Zbl 0718.76035McLachlan, Robert I. 3 1991 Discrete mechanics and optimal control for image registration. Zbl 1334.94035McLachlan, Robert I.; Marsland, Stephen 3 2007 Asymptotic blowup profiles for modified Camassa-Holm equations. Zbl 1234.35208McLachlan, Robert I.; Zhang, Xingyou 3 2011 Structure-preserving deep learning. Zbl 07440570Celledoni, E.; Ehrhardt, M. J.; Etmann, C.; McLachlan, R. I.; Owren, B.; Schonlieb, C.-B.; Sherry, F. 3 2021 The Kelvin-Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms. Zbl 1210.37049McLachlan, Robert I.; Marsland, Stephen R. 2 2006 Geodesic warps by conformal mappings. Zbl 1304.92077Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew 2 2013 Hamiltonian finite-dimensional models of baroclinic instability. Zbl 1024.86500McLachlan, R. I.; Szunyogh, I.; Zeitlin, V. 2 1997 Numerical integrators that contract volume. Zbl 0951.65139McLachlan, Robert I.; Quispel, G. R. W. 2 2000 On conjugate B-series and their geometric structure. Zbl 1432.65184Celledoni, E.; McLachlan, R. I.; Owren, B.; Quispel, G. R. W. 2 2010 Currents and finite elements as tools for shape space. Zbl 1468.65018Benn, James; Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 2 2019 Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. Zbl 1407.37089McLachlan, Robert I.; Offen, Christian 2 2018 Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations. Zbl 1472.65112McDonald, Fleur; McLachlan, Robert I.; Moore, Brian E.; Quispel, G. R. W. 2 2016 Explicit symplectic splitting methods applied to PDE’s. Zbl 0788.65095McLachlan, Robert I. 1 1993 A steady separated viscous corner flow. Zbl 0731.76025McLachlan, Robert 1 1991 The structure of a set of vector fields on Poisson manifolds. Zbl 1162.53061McLachlan, Robert I. 1 2009 The algebraic entropy of classical mechanics. Zbl 1062.70035McLachlan, Robert I.; Ryland, Brett 1 2003 On conformal variational problems and free boundary continua. Zbl 1287.35107Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew 1 2014 Preservation of bifurcations of Hamiltonian boundary value problems under discretisation. Zbl 1455.65114McLachlan, Robert I.; Offen, Christian 1 2020 Reconsidering trigonometric integrators. Zbl 1178.65142O’Neale, Dion R. J.; McLachlan, Robert I. 1 2009 Preservation and destruction of periodic orbits by symplectic integrators. Zbl 1196.65191McLachlan, Robert I.; O’Neale, Dion R. J. 1 2010 The Lie algebra of classical mechanics. Zbl 1431.17004McLachlan, Robert I.; Murua, Ander 1 2019 Principal symmetric space analysis. Zbl 1437.62217Curry, Charles; Marsland, Stephen; McLachlan, Robert I. 1 2019 Symplectic integration of boundary value problems. Zbl 1480.65367McLachlan, Robert I.; Offen, Christian 1 2019 Möbius invariants of shapes and images. Zbl 1386.68181Marsland, Stephen; McLachlan, Robert I. 1 2016 Symplectic integrators for index 1 constraints. Zbl 1287.65138Mclachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt 1 2013 Geometry of discrete-time spin systems. Zbl 1352.37190McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 1 2016 Structure-preserving deep learning. Zbl 07440570Celledoni, E.; Ehrhardt, M. J.; Etmann, C.; McLachlan, R. I.; Owren, B.; Schonlieb, C.-B.; Sherry, F. 3 2021 Multisymplecticity of hybridizable discontinuous Galerkin methods. Zbl 1472.65147Mclachlan, Robert I.; Stern, Ari 4 2020 Preservation of bifurcations of Hamiltonian boundary value problems under discretisation. Zbl 1455.65114McLachlan, Robert I.; Offen, Christian 1 2020 Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation. Zbl 1422.70012van der Kamp, Peter H.; Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W. 7 2019 Currents and finite elements as tools for shape space. Zbl 1468.65018Benn, James; Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 2 2019 The Lie algebra of classical mechanics. Zbl 1431.17004McLachlan, Robert I.; Murua, Ander 1 2019 Principal symmetric space analysis. Zbl 1437.62217Curry, Charles; Marsland, Stephen; McLachlan, Robert I. 1 2019 Symplectic integration of boundary value problems. Zbl 1480.65367McLachlan, Robert I.; Offen, Christian 1 2019 Bifurcation of solutions to Hamiltonian boundary value problems. Zbl 1402.37067Mclachlan, R. I.; Offen, C. 5 2018 Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. Zbl 1407.37089McLachlan, Robert I.; Offen, Christian 2 2018 A minimal-variable symplectic integrator on spheres. Zbl 1364.37166McLachlan, Robert; Modin, Klas; Verdier, Olivier 9 2017 Discrete gradient methods for solving variational image regularisation models. Zbl 1371.94146Grimm, V.; McLachlan, Robert I.; McLaren, David I.; Quispel, G. R. W.; Schönlieb, C.-B. 7 2017 B-series methods are exactly the affine equivariant methods. Zbl 1364.65145McLachlan, Robert I.; Modin, Klas; Munthe-Kaas, Hans; Verdier, Olivier 12 2016 Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations. Zbl 1472.65112McDonald, Fleur; McLachlan, Robert I.; Moore, Brian E.; Quispel, G. R. W. 2 2016 Möbius invariants of shapes and images. Zbl 1386.68181Marsland, Stephen; McLachlan, Robert I. 1 2016 Geometry of discrete-time spin systems. Zbl 1352.37190McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 1 2016 Discretization of polynomial vector fields by polarization. Zbl 1372.65201Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W. 9 2015 The multisymplectic diamond scheme. Zbl 1334.37095McLachlan, R. I.; Wilkins, M. C. 6 2015 Collective Lie-Poisson integrators on \(\mathbb{R}^{3}\). Zbl 1318.65079McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 5 2015 Discrete gradient methods have an energy conservation law. Zbl 1282.65112McLachlan, Robert I.; Quispel, G. R. W. 19 2014 Integrability properties of Kahan’s method. Zbl 1336.37045Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W. 17 2014 High order multisymplectic Runge-Kutta methods. Zbl 1310.37044McLachlan, Robert I.; Ryland, Brett N.; Sun, Yajuan 13 2014 Modified trigonometric integrators. Zbl 1320.65194McLachlan, Robert I.; Stern, Ari 11 2014 Collective symplectic integrators. Zbl 1333.65139McLachlan, Robert I.; Modin, Klas; Verdier, Olivier 8 2014 Geometric generalisations of SHAKE and RATTLE. Zbl 1347.37131McLachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt 7 2014 On conformal variational problems and free boundary continua. Zbl 1287.35107Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew 1 2014 Geodesic warps by conformal mappings. Zbl 1304.92077Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew 2 2013 Symplectic integrators for index 1 constraints. Zbl 1287.65138Mclachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt 1 2013 Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Zbl 1284.65184Celledoni, E.; Grimm, V.; McLachlan, R. I.; McLaren, D. I.; O’Neale, D.; Owren, B.; Quispel, G. R. W. 115 2012 Geometric properties of Kahan’s method. Zbl 1278.65192Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W. 26 2012 On Euler-Arnold equations and totally geodesic subgroups. Zbl 1221.53118Modin, Klas; Perlmutter, Matthew; Marsland, Stephen; McLachlan, Robert 11 2011 Linear stability of partitioned Runge-Kutta methods. Zbl 1228.65124McLachlan, R. I.; Sun, Y.; Tse, P. S. P. 7 2011 Asymptotic blowup profiles for modified Camassa-Holm equations. Zbl 1234.35208McLachlan, Robert I.; Zhang, Xingyou 3 2011 Energy-preserving integrators and the structure of B-series. Zbl 1205.65325Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W. 25 2010 Exploiting the Hamiltonian structure of a neural field model. Zbl 1203.37034Elvin, A. J.; Laing, C. R.; McLachlan, R. I.; Roberts, M. G. 10 2010 On conjugate B-series and their geometric structure. Zbl 1432.65184Celledoni, E.; McLachlan, R. I.; Owren, B.; Quispel, G. R. W. 2 2010 Preservation and destruction of periodic orbits by symplectic integrators. Zbl 1196.65191McLachlan, Robert I.; O’Neale, Dion R. J. 1 2010 Energy-preserving Runge-Kutta methods. Zbl 1169.65348Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. Reinout W.; Wright, William M. 47 2009 Well-posedness of modified Camassa-Holm equations. Zbl 1203.35079McLachlan, Robert; Zhang, Xingyou 21 2009 Linearization-preserving self-adjoint and symplectic integrators. Zbl 1162.65411McLachlan, R. I.; Quispel, G. R. W.; Tse, P. S. P. 11 2009 On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D. 10 2009 The structure of a set of vector fields on Poisson manifolds. Zbl 1162.53061McLachlan, Robert I. 1 2009 Reconsidering trigonometric integrators. Zbl 1178.65142O’Neale, Dion R. J.; McLachlan, Robert I. 1 2009 Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058Hairer, E.; McLachlan, R. I.; Razakarivony, A. 20 2008 Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. Zbl 1147.65053McLachlan, R. I.; Munthe-Kaas, H. Z.; Quispel, G. R. W.; Zanna, A. 7 2008 On multisymplecticity of partitioned Runge-Kutta methods. Zbl 1172.37030Ryland, Brett N.; McLachlan, Robert I. 7 2008 On the multisymplecticity of partitioned Runge-Kutta and splitting methods. Zbl 1125.65115Ryland, Brett N.; McLachlan, Robert I.; Frank, Jason 17 2007 \(N\)-particle dynamics of the Euler equations for planar diffeomorphisms. Zbl 1149.37038McLachlan, Robert I.; Marsland, Stephen 5 2007 A new implementation of symplectic Runge-Kutta methods. Zbl 1145.65111McLachlan, Robert I. 5 2007 Discrete mechanics and optimal control for image registration. Zbl 1334.94035McLachlan, Robert I.; Marsland, Stephen 3 2007 Geometric numerical integration of differential equations. Zbl 1092.65055McLachlan, Robert; Quispel, Reinout 46 2006 Integrators for nonholonomic mechanical systems. Zbl 1104.37043McLachlan, R.; Perlmutter, M. 31 2006 The Kelvin-Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms. Zbl 1210.37049McLachlan, Robert I.; Marsland, Stephen R. 2 2006 On symplectic and multisymplectic schemes for the KdV equation. Zbl 1203.65277Ascher, U. M.; Mclachlan, R. I. 40 2005 The discrete Moser-Veselov algorithm for the free rigid body, revisited. Zbl 1123.70012McLachlan, Robert I.; Zanna, Antonella 11 2005 Multisymplectic box schemes and the Korteweg-de Vries equation. Zbl 1038.65138Ascher, Uri M.; McLachlan, Robert I. 64 2004 Energy drift in reversible time integration. Zbl 1064.37063McLachlan, R. I.; Perlmutter, M. 6 2004 Explicit geometric integration of polynomial vector fields. Zbl 1066.65150McLachlan, Robert I.; Quispel, G. Reinout W. 5 2004 On the nonlinear stability of symplectic integrators. Zbl 1070.65130McLachlan, Robert I.; Perlmutter, Matthew; Quispel, G. R. W. 3 2004 Skew-adjoint finite difference methods on nonuniform grids. Zbl 1073.65084Kitson, Adrian; McLachlan, Robert I.; Robidoux, Nicolas 8 2003 Geometric integration of conservative polynomial ODEs. Zbl 1021.65064McLachlan, Robert I.; Quispel, G. R. W. 5 2003 Spatial discretization of partial differential equations with integrals. Zbl 1080.65076McLachlan, Robert I. 5 2003 The algebraic entropy of classical mechanics. Zbl 1062.70035McLachlan, Robert I.; Ryland, Brett 1 2003 Splitting methods. Zbl 1105.65341McLachlan, Robert I.; Quispel, G. Reinout W. 222 2002 Families of high-order composition methods. Zbl 1016.65044McLachlan, Robert I. 10 2002 Conformal Hamiltonian systems. Zbl 1005.53058McLachlan, Robert; Perlmutter, Matthew 31 2001 What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration. Zbl 0994.65138McLachlan, Robert I.; Quispel, G. R. W. 17 2001 Six lectures on the geometric integration of ODEs. Zbl 0978.65056McLachlan, Robert; Quispel, Reinout 16 2001 Antisymmetry, pseudospectral methods, and conservative PDEs. Zbl 0963.65105McLachlan, Robert I.; Robidoux, Nicolas 6 2000 Numerical integrators that contract volume. Zbl 0951.65139McLachlan, Robert I.; Quispel, G. R. W. 2 2000 Geometric integration using discrete gradients. Zbl 0933.65143McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas 177 1999 Approximately preserving symmetries in the numerical integration of ordinary differential equations. Zbl 0939.65139Iserles, Arieh; McLachlan, Robert; Zanna, Antonella 7 1999 Area preservation in computational fluid dynamics. Zbl 0966.76073McLachlan, Robert I. 4 1999 Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals. Zbl 1042.37522McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas 32 1998 Numerical integrators that preserve symmetries and reversing symmetries. Zbl 0912.34015McLachlan, R. I.; Quispel, G. R. W.; Turner, G. S. 21 1998 Generating functions for dynamical systems with symmetries, integrals, and differential invariants. Zbl 1194.37089Mclachlan, Robert I.; Quispel, G. R. W. 6 1998 Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation. Zbl 0888.65095McLachlan, Robert I.; Gray, Stephen K. 6 1997 Hamiltonian finite-dimensional models of baroclinic instability. Zbl 1024.86500McLachlan, R. I.; Szunyogh, I.; Zeitlin, V. 2 1997 A survey of open problems in symplectic integration. Zbl 0871.65058McLachlan, Robert I.; Scovel, Clint 23 1996 More on symplectic correctors. Zbl 0872.65060McLachlan, Robert I. 5 1996 On the numerical integration of ordinary differential equations by symmetric composition methods. Zbl 0821.65048McLachlan, Robert I. 100 1995 Composition methods in the presence of small parameters. Zbl 0832.65071McLachlan, Robert I. 24 1995 Equivariant constrained symplectic integration. Zbl 0836.58017McLachlan, R. I.; Scovel, C. 16 1995 Comment on “Poisson schemes for Hamiltonian systems on Poisson manifolds”. Zbl 0821.58020McLachlan, R. 4 1995 Symplectic integration of Hamiltonian wave equations. Zbl 0831.65099McLachlan, Robert 69 1994 Global behavior of the charged isosceles three-body problem. Zbl 0900.70157Atela, Pau; McLachlan, Robert I. 10 1994 A gallery of constant-negative-curvature surfaces. Zbl 0812.53003McLachlan, Robert 6 1994 A note on the motion of surfaces. Zbl 0961.53500McLachlan, Robert I.; Segur, Harvey 4 1994 Explicit Lie-Poisson integration and the Euler equations. Zbl 0972.65509McLachlan, Robert I. 37 1993 Explicit symplectic splitting methods applied to PDE’s. Zbl 0788.65095McLachlan, Robert I. 1 1993 The accuracy of symplectic integrators. Zbl 0747.58032McLachlan, Robert I.; Atela, Pau 63 1992 The boundary layer on a finite flat plate. Zbl 0718.76035McLachlan, Robert I. 3 1991 A steady separated viscous corner flow. Zbl 0731.76025McLachlan, Robert 1 1991 all cited Publications top 5 cited Publications all top 5 Cited by 1,227 Authors 41 McLachlan, Robert I. 32 Wang, Yushun 26 Blanes, Sergio 26 Quispel, Gilles Reinout Willem 23 Celledoni, Elena 21 Karasözen, Bülent 21 Wu, Xinyuan 19 Matsuo, Takayasu 19 Owren, Brynjulf 18 Casas, Fernando 16 Miyatake, Yuto 16 Song, Songhe 15 Cai, Jiaxiang 15 Cai, Wenjun 15 Modin, Klas 15 Sun, Yajuan 14 Wang, Bin 12 Hairer, Ernst 12 Martín de Diego, David 12 Murua, Ander 12 Zanna, Antonella 10 Brugnano, Luigi 10 Hong, Jialin 10 Iserles, Arieh 10 Li, Haochen 10 Qian, Xu 10 Verdier, Olivier 9 Bao, Weizhu 9 Geiser, Jürgen 9 Ostermann, Alexander 9 Uzunca, Murat 9 Vilmart, Gilles 8 Bader, Philipp 8 Ding, Xiaohua 8 Furihata, Daisuke 8 Gong, Yuezheng 8 Iavernaro, Felice 8 Leok, Melvin 8 McLaren, David I. 8 Shi, Wei 8 Thalhammer, Mechthild 8 Zhang, Shengliang 7 Cieśliński, Jan L. 7 Jiang, Chaolong 7 Kong, Linghua 7 Liu, Kai 7 Ma, Qiang 7 Marsland, Stephen R. 7 Moore, Brian E. 7 Munthe-Kaas, Hans Z. 7 Petrera, Matteo 7 Sanz-Serna, Jesús María 7 Simos, Theodore E. 7 Suris, Yuri Borisovich 7 Tang, Wensheng 7 Zhang, Hong 6 Aydin, Ayhan 6 Chartier, Philippe 6 de León Rodríguez, Manuel 6 Frank, Jason 6 Kalogiratou, Zacharoula 6 Portillo, A. M. 6 Qin, Mengzhao 6 Sato, Shun 6 Schratz, Katharina 6 Song, Yongzhong 6 Tang, Yifa 6 Trigiante, Donato 6 Zhang, Jingjing 5 Butcher, John C. 5 Calvo, Manuel 5 Chin, Siu A. 5 D’Ambrosio, Raffaele 5 Eidnes, Sølve 5 Elenin, G. G. 5 Elenina, T. G. 5 Faou, Erwan 5 Guha, Partha 5 He, Yang 5 Leoncini, Xavier 5 Liang, Dong 5 Liu, Changying 5 Lubich, Christian 5 Luo, Albert C. J. 5 Makazaga, Joseba 5 Mei, Lijie 5 Montijano, Juan Ignacio 5 Rández, Luis 5 Schönlieb, Carola-Bibiane 5 Viviani, Milo 5 Wang, Lijin 5 Wang, Qi 5 Yaguchi, Takaharu 4 Auzinger, Winfried 4 Bhatt, Ashish 4 Grimm, Volker 4 Holm, Darryl D. 4 Huang, Li 4 Hydon, Peter Ellsworth 4 Koch, Othmar ...and 1,127 more Authors all top 5 Cited in 216 Serials 106 Journal of Computational Physics 65 Journal of Computational and Applied Mathematics 50 Applied Mathematics and Computation 48 Applied Numerical Mathematics 38 BIT 25 Foundations of Computational Mathematics 23 Journal of Scientific Computing 21 Journal of Mathematical Physics 20 International Journal of Computer Mathematics 19 Mathematics of Computation 19 SIAM Journal on Scientific Computing 18 Computers & Mathematics with Applications 18 Numerische Mathematik 17 Computer Physics Communications 17 Numerical Algorithms 15 Physica D 15 Journal of Computational Dynamics 14 Discrete and Continuous Dynamical Systems 14 Communications in Nonlinear Science and Numerical Simulation 13 Mathematics and Computers in Simulation 13 SIAM Journal on Numerical Analysis 13 Journal of Nonlinear Science 12 Journal of Geometry and Physics 12 Advances in Computational Mathematics 10 Applied Mathematics Letters 10 Celestial Mechanics and Dynamical Astronomy 9 Journal of Mathematical Analysis and Applications 8 Computer Methods in Applied Mechanics and Engineering 8 Physics Letters. A 8 Communications in Computational Physics 7 Chaos, Solitons and Fractals 7 Japan Journal of Industrial and Applied Mathematics 7 Advances in Applied Mathematics and Mechanics 6 Nonlinearity 6 Numerical Methods for Partial Differential Equations 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Chaos 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Journal of Geometric Mechanics 6 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 5 Journal of Fluid Mechanics 5 Calcolo 5 Journal of Differential Equations 5 Engineering Analysis with Boundary Elements 5 Journal of Mathematical Chemistry 5 International Journal of Modern Physics C 5 SIAM Journal on Applied Dynamical Systems 5 SIAM Journal on Imaging Sciences 4 International Journal for Numerical Methods in Engineering 4 Computational Mechanics 4 Journal of Mathematical Imaging and Vision 4 Journal of Physics A: Mathematical and Theoretical 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Acta Mechanica 3 Computers and Fluids 3 International Journal for Numerical Methods in Fluids 3 Journal of Statistical Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Advances in Mathematics 3 Automatica 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Systems & Control Letters 3 Acta Mathematicae Applicatae Sinica. English Series 3 Applied Mathematical Modelling 3 International Journal of Computer Vision 3 Mathematical Physics, Analysis and Geometry 3 Differential Equations 3 Discrete and Continuous Dynamical Systems. Series B 3 Acta Numerica 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Statistics and Computing 3 JSIAM Letters 2 Classical and Quantum Gravity 2 Journal of Approximation Theory 2 Applied Mathematics and Mechanics. (English Edition) 2 Journal of Computational Mathematics 2 Mathematical and Computer Modelling 2 European Journal of Applied Mathematics 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Computational Mathematics and Mathematical Physics 2 Journal of Dynamics and Differential Equations 2 Physics of Fluids 2 Computational and Applied Mathematics 2 Filomat 2 Journal of Difference Equations and Applications 2 Mathematical Problems in Engineering 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Multibody System Dynamics 2 Abstract and Applied Analysis 2 New Journal of Physics 2 LMS Journal of Computation and Mathematics 2 Nonlinear Analysis. Real World Applications 2 Journal of Evolution Equations 2 Mediterranean Journal of Mathematics 2 Journal of Statistical Mechanics: Theory and Experiment 2 Discrete and Continuous Dynamical Systems. Series S 2 East Asian Journal on Applied Mathematics 2 SIAM/ASA Journal on Uncertainty Quantification 2 Nonlinear Analysis. Theory, Methods & Applications 2 Arnold Mathematical Journal ...and 116 more Serials all top 5 Cited in 52 Fields 762 Numerical analysis (65-XX) 360 Dynamical systems and ergodic theory (37-XX) 329 Partial differential equations (35-XX) 157 Mechanics of particles and systems (70-XX) 116 Ordinary differential equations (34-XX) 100 Fluid mechanics (76-XX) 50 Differential geometry (53-XX) 41 Statistical mechanics, structure of matter (82-XX) 40 Quantum theory (81-XX) 39 Probability theory and stochastic processes (60-XX) 37 Optics, electromagnetic theory (78-XX) 33 Biology and other natural sciences (92-XX) 25 Difference and functional equations (39-XX) 24 Mechanics of deformable solids (74-XX) 21 Topological groups, Lie groups (22-XX) 21 Global analysis, analysis on manifolds (58-XX) 20 Computer science (68-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 15 Operator theory (47-XX) 14 Systems theory; control (93-XX) 13 Algebraic geometry (14-XX) 13 Approximations and expansions (41-XX) 11 Nonassociative rings and algebras (17-XX) 10 Statistics (62-XX) 10 Geophysics (86-XX) 9 Operations research, mathematical programming (90-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Relativity and gravitational theory (83-XX) 7 General and overarching topics; collections (00-XX) 7 Combinatorics (05-XX) 7 Associative rings and algebras (16-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Integral equations (45-XX) 5 Information and communication theory, circuits (94-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Real functions (26-XX) 3 Astronomy and astrophysics (85-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Functional analysis (46-XX) 2 Algebraic topology (55-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year