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McLachlan, Robert I.

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Author ID: mclachlan.robert-i Recent zbMATH articles by "McLachlan, Robert I."
Published as: McLachlan, Robert I.; McLachlan, R. I.; McLachlan, Robert; Mclachlan, Robert I.; Mclachlan, R. I.; McLachlan, R.
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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

Publications by Year

Citations contained in zbMATH Open

93 Publications have been cited 1,665 times in 1,044 Documents Cited by Year
Splitting methods. Zbl 1105.65341
McLachlan, Robert I.; Quispel, G. Reinout W.
222
2002
Geometric integration using discrete gradients. Zbl 0933.65143
McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas
177
1999
Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Zbl 1284.65184
Celledoni, 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 0821.65048
McLachlan, Robert I.
100
1995
Symplectic integration of Hamiltonian wave equations. Zbl 0831.65099
McLachlan, Robert
69
1994
Multisymplectic box schemes and the Korteweg-de Vries equation. Zbl 1038.65138
Ascher, Uri M.; McLachlan, Robert I.
64
2004
The accuracy of symplectic integrators. Zbl 0747.58032
McLachlan, Robert I.; Atela, Pau
63
1992
Energy-preserving Runge-Kutta methods. Zbl 1169.65348
Celledoni, 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 1092.65055
McLachlan, Robert; Quispel, Reinout
46
2006
On symplectic and multisymplectic schemes for the KdV equation. Zbl 1203.65277
Ascher, U. M.; Mclachlan, R. I.
40
2005
Explicit Lie-Poisson integration and the Euler equations. Zbl 0972.65509
McLachlan, Robert I.
37
1993
Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals. Zbl 1042.37522
McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas
32
1998
Conformal Hamiltonian systems. Zbl 1005.53058
McLachlan, Robert; Perlmutter, Matthew
31
2001
Integrators for nonholonomic mechanical systems. Zbl 1104.37043
McLachlan, R.; Perlmutter, M.
31
2006
Geometric properties of Kahan’s method. Zbl 1278.65192
Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W.
26
2012
Energy-preserving integrators and the structure of B-series. Zbl 1205.65325
Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W.
25
2010
Composition methods in the presence of small parameters. Zbl 0832.65071
McLachlan, Robert I.
24
1995
A survey of open problems in symplectic integration. Zbl 0871.65058
McLachlan, Robert I.; Scovel, Clint
23
1996
Numerical integrators that preserve symmetries and reversing symmetries. Zbl 0912.34015
McLachlan, R. I.; Quispel, G. R. W.; Turner, G. S.
21
1998
Well-posedness of modified Camassa-Holm equations. Zbl 1203.35079
McLachlan, Robert; Zhang, Xingyou
21
2009
Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058
Hairer, E.; McLachlan, R. I.; Razakarivony, A.
20
2008
Discrete gradient methods have an energy conservation law. Zbl 1282.65112
McLachlan, Robert I.; Quispel, G. R. W.
19
2014
What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration. Zbl 0994.65138
McLachlan, Robert I.; Quispel, G. R. W.
17
2001
On the multisymplecticity of partitioned Runge-Kutta and splitting methods. Zbl 1125.65115
Ryland, Brett N.; McLachlan, Robert I.; Frank, Jason
17
2007
Integrability properties of Kahan’s method. Zbl 1336.37045
Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
17
2014
Equivariant constrained symplectic integration. Zbl 0836.58017
McLachlan, R. I.; Scovel, C.
16
1995
Six lectures on the geometric integration of ODEs. Zbl 0978.65056
McLachlan, Robert; Quispel, Reinout
16
2001
High order multisymplectic Runge-Kutta methods. Zbl 1310.37044
McLachlan, Robert I.; Ryland, Brett N.; Sun, Yajuan
13
2014
B-series methods are exactly the affine equivariant methods. Zbl 1364.65145
McLachlan, Robert I.; Modin, Klas; Munthe-Kaas, Hans; Verdier, Olivier
12
2016
The discrete Moser-Veselov algorithm for the free rigid body, revisited. Zbl 1123.70012
McLachlan, Robert I.; Zanna, Antonella
11
2005
Linearization-preserving self-adjoint and symplectic integrators. Zbl 1162.65411
McLachlan, R. I.; Quispel, G. R. W.; Tse, P. S. P.
11
2009
Modified trigonometric integrators. Zbl 1320.65194
McLachlan, Robert I.; Stern, Ari
11
2014
On Euler-Arnold equations and totally geodesic subgroups. Zbl 1221.53118
Modin, Klas; Perlmutter, Matthew; Marsland, Stephen; McLachlan, Robert
11
2011
Exploiting the Hamiltonian structure of a neural field model. Zbl 1203.37034
Elvin, A. J.; Laing, C. R.; McLachlan, R. I.; Roberts, M. G.
10
2010
Families of high-order composition methods. Zbl 1016.65044
McLachlan, Robert I.
10
2002
Global behavior of the charged isosceles three-body problem. Zbl 0900.70157
Atela, Pau; McLachlan, Robert I.
10
1994
On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067
Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D.
10
2009
Discretization of polynomial vector fields by polarization. Zbl 1372.65201
Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
9
2015
A minimal-variable symplectic integrator on spheres. Zbl 1364.37166
McLachlan, Robert; Modin, Klas; Verdier, Olivier
9
2017
Collective symplectic integrators. Zbl 1333.65139
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
8
2014
Skew-adjoint finite difference methods on nonuniform grids. Zbl 1073.65084
Kitson, Adrian; McLachlan, Robert I.; Robidoux, Nicolas
8
2003
Approximately preserving symmetries in the numerical integration of ordinary differential equations. Zbl 0939.65139
Iserles, Arieh; McLachlan, Robert; Zanna, Antonella
7
1999
Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. Zbl 1147.65053
McLachlan, R. I.; Munthe-Kaas, H. Z.; Quispel, G. R. W.; Zanna, A.
7
2008
On multisymplecticity of partitioned Runge-Kutta methods. Zbl 1172.37030
Ryland, Brett N.; McLachlan, Robert I.
7
2008
Geometric generalisations of SHAKE and RATTLE. Zbl 1347.37131
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt
7
2014
Discrete gradient methods for solving variational image regularisation models. Zbl 1371.94146
Grimm, 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 1422.70012
van 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 1228.65124
McLachlan, R. I.; Sun, Y.; Tse, P. S. P.
7
2011
The multisymplectic diamond scheme. Zbl 1334.37095
McLachlan, R. I.; Wilkins, M. C.
6
2015
Antisymmetry, pseudospectral methods, and conservative PDEs. Zbl 0963.65105
McLachlan, Robert I.; Robidoux, Nicolas
6
2000
A gallery of constant-negative-curvature surfaces. Zbl 0812.53003
McLachlan, Robert
6
1994
Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation. Zbl 0888.65095
McLachlan, Robert I.; Gray, Stephen K.
6
1997
Generating functions for dynamical systems with symmetries, integrals, and differential invariants. Zbl 1194.37089
Mclachlan, Robert I.; Quispel, G. R. W.
6
1998
Energy drift in reversible time integration. Zbl 1064.37063
McLachlan, R. I.; Perlmutter, M.
6
2004
Collective Lie-Poisson integrators on \(\mathbb{R}^{3}\). Zbl 1318.65079
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
5
2015
Geometric integration of conservative polynomial ODEs. Zbl 1021.65064
McLachlan, Robert I.; Quispel, G. R. W.
5
2003
\(N\)-particle dynamics of the Euler equations for planar diffeomorphisms. Zbl 1149.37038
McLachlan, Robert I.; Marsland, Stephen
5
2007
More on symplectic correctors. Zbl 0872.65060
McLachlan, Robert I.
5
1996
A new implementation of symplectic Runge-Kutta methods. Zbl 1145.65111
McLachlan, Robert I.
5
2007
Explicit geometric integration of polynomial vector fields. Zbl 1066.65150
McLachlan, Robert I.; Quispel, G. Reinout W.
5
2004
Spatial discretization of partial differential equations with integrals. Zbl 1080.65076
McLachlan, Robert I.
5
2003
Bifurcation of solutions to Hamiltonian boundary value problems. Zbl 1402.37067
Mclachlan, R. I.; Offen, C.
5
2018
A note on the motion of surfaces. Zbl 0961.53500
McLachlan, Robert I.; Segur, Harvey
4
1994
Area preservation in computational fluid dynamics. Zbl 0966.76073
McLachlan, Robert I.
4
1999
Comment on “Poisson schemes for Hamiltonian systems on Poisson manifolds”. Zbl 0821.58020
McLachlan, R.
4
1995
Multisymplecticity of hybridizable discontinuous Galerkin methods. Zbl 1472.65147
Mclachlan, Robert I.; Stern, Ari
4
2020
On the nonlinear stability of symplectic integrators. Zbl 1070.65130
McLachlan, Robert I.; Perlmutter, Matthew; Quispel, G. R. W.
3
2004
The boundary layer on a finite flat plate. Zbl 0718.76035
McLachlan, Robert I.
3
1991
Discrete mechanics and optimal control for image registration. Zbl 1334.94035
McLachlan, Robert I.; Marsland, Stephen
3
2007
Asymptotic blowup profiles for modified Camassa-Holm equations. Zbl 1234.35208
McLachlan, Robert I.; Zhang, Xingyou
3
2011
Structure-preserving deep learning. Zbl 07440570
Celledoni, 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 1210.37049
McLachlan, Robert I.; Marsland, Stephen R.
2
2006
Geodesic warps by conformal mappings. Zbl 1304.92077
Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew
2
2013
Hamiltonian finite-dimensional models of baroclinic instability. Zbl 1024.86500
McLachlan, R. I.; Szunyogh, I.; Zeitlin, V.
2
1997
Numerical integrators that contract volume. Zbl 0951.65139
McLachlan, Robert I.; Quispel, G. R. W.
2
2000
On conjugate B-series and their geometric structure. Zbl 1432.65184
Celledoni, E.; McLachlan, R. I.; Owren, B.; Quispel, G. R. W.
2
2010
Currents and finite elements as tools for shape space. Zbl 1468.65018
Benn, James; Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
2
2019
Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. Zbl 1407.37089
McLachlan, Robert I.; Offen, Christian
2
2018
Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations. Zbl 1472.65112
McDonald, Fleur; McLachlan, Robert I.; Moore, Brian E.; Quispel, G. R. W.
2
2016
Explicit symplectic splitting methods applied to PDE’s. Zbl 0788.65095
McLachlan, Robert I.
1
1993
A steady separated viscous corner flow. Zbl 0731.76025
McLachlan, Robert
1
1991
The structure of a set of vector fields on Poisson manifolds. Zbl 1162.53061
McLachlan, Robert I.
1
2009
The algebraic entropy of classical mechanics. Zbl 1062.70035
McLachlan, Robert I.; Ryland, Brett
1
2003
On conformal variational problems and free boundary continua. Zbl 1287.35107
Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew
1
2014
Preservation of bifurcations of Hamiltonian boundary value problems under discretisation. Zbl 1455.65114
McLachlan, Robert I.; Offen, Christian
1
2020
Reconsidering trigonometric integrators. Zbl 1178.65142
O’Neale, Dion R. J.; McLachlan, Robert I.
1
2009
Preservation and destruction of periodic orbits by symplectic integrators. Zbl 1196.65191
McLachlan, Robert I.; O’Neale, Dion R. J.
1
2010
The Lie algebra of classical mechanics. Zbl 1431.17004
McLachlan, Robert I.; Murua, Ander
1
2019
Principal symmetric space analysis. Zbl 1437.62217
Curry, Charles; Marsland, Stephen; McLachlan, Robert I.
1
2019
Symplectic integration of boundary value problems. Zbl 1480.65367
McLachlan, Robert I.; Offen, Christian
1
2019
Möbius invariants of shapes and images. Zbl 1386.68181
Marsland, Stephen; McLachlan, Robert I.
1
2016
Symplectic integrators for index 1 constraints. Zbl 1287.65138
Mclachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt
1
2013
Geometry of discrete-time spin systems. Zbl 1352.37190
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
1
2016
Structure-preserving deep learning. Zbl 07440570
Celledoni, 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 1472.65147
Mclachlan, Robert I.; Stern, Ari
4
2020
Preservation of bifurcations of Hamiltonian boundary value problems under discretisation. Zbl 1455.65114
McLachlan, 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 1422.70012
van 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 1468.65018
Benn, James; Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
2
2019
The Lie algebra of classical mechanics. Zbl 1431.17004
McLachlan, Robert I.; Murua, Ander
1
2019
Principal symmetric space analysis. Zbl 1437.62217
Curry, Charles; Marsland, Stephen; McLachlan, Robert I.
1
2019
Symplectic integration of boundary value problems. Zbl 1480.65367
McLachlan, Robert I.; Offen, Christian
1
2019
Bifurcation of solutions to Hamiltonian boundary value problems. Zbl 1402.37067
Mclachlan, R. I.; Offen, C.
5
2018
Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. Zbl 1407.37089
McLachlan, Robert I.; Offen, Christian
2
2018
A minimal-variable symplectic integrator on spheres. Zbl 1364.37166
McLachlan, Robert; Modin, Klas; Verdier, Olivier
9
2017
Discrete gradient methods for solving variational image regularisation models. Zbl 1371.94146
Grimm, 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 1364.65145
McLachlan, Robert I.; Modin, Klas; Munthe-Kaas, Hans; Verdier, Olivier
12
2016
Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations. Zbl 1472.65112
McDonald, Fleur; McLachlan, Robert I.; Moore, Brian E.; Quispel, G. R. W.
2
2016
Möbius invariants of shapes and images. Zbl 1386.68181
Marsland, Stephen; McLachlan, Robert I.
1
2016
Geometry of discrete-time spin systems. Zbl 1352.37190
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
1
2016
Discretization of polynomial vector fields by polarization. Zbl 1372.65201
Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
9
2015
The multisymplectic diamond scheme. Zbl 1334.37095
McLachlan, R. I.; Wilkins, M. C.
6
2015
Collective Lie-Poisson integrators on \(\mathbb{R}^{3}\). Zbl 1318.65079
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
5
2015
Discrete gradient methods have an energy conservation law. Zbl 1282.65112
McLachlan, Robert I.; Quispel, G. R. W.
19
2014
Integrability properties of Kahan’s method. Zbl 1336.37045
Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
17
2014
High order multisymplectic Runge-Kutta methods. Zbl 1310.37044
McLachlan, Robert I.; Ryland, Brett N.; Sun, Yajuan
13
2014
Modified trigonometric integrators. Zbl 1320.65194
McLachlan, Robert I.; Stern, Ari
11
2014
Collective symplectic integrators. Zbl 1333.65139
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
8
2014
Geometric generalisations of SHAKE and RATTLE. Zbl 1347.37131
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt
7
2014
On conformal variational problems and free boundary continua. Zbl 1287.35107
Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew
1
2014
Geodesic warps by conformal mappings. Zbl 1304.92077
Marsland, Stephen; McLachlan, Robert I.; Modin, Klas; Perlmutter, Matthew
2
2013
Symplectic integrators for index 1 constraints. Zbl 1287.65138
Mclachlan, Robert I.; Modin, Klas; Verdier, Olivier; Wilkins, Matt
1
2013
Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Zbl 1284.65184
Celledoni, 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 1278.65192
Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W.
26
2012
On Euler-Arnold equations and totally geodesic subgroups. Zbl 1221.53118
Modin, Klas; Perlmutter, Matthew; Marsland, Stephen; McLachlan, Robert
11
2011
Linear stability of partitioned Runge-Kutta methods. Zbl 1228.65124
McLachlan, R. I.; Sun, Y.; Tse, P. S. P.
7
2011
Asymptotic blowup profiles for modified Camassa-Holm equations. Zbl 1234.35208
McLachlan, Robert I.; Zhang, Xingyou
3
2011
Energy-preserving integrators and the structure of B-series. Zbl 1205.65325
Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf; Quispel, G. R. W.
25
2010
Exploiting the Hamiltonian structure of a neural field model. Zbl 1203.37034
Elvin, A. J.; Laing, C. R.; McLachlan, R. I.; Roberts, M. G.
10
2010
On conjugate B-series and their geometric structure. Zbl 1432.65184
Celledoni, E.; McLachlan, R. I.; Owren, B.; Quispel, G. R. W.
2
2010
Preservation and destruction of periodic orbits by symplectic integrators. Zbl 1196.65191
McLachlan, Robert I.; O’Neale, Dion R. J.
1
2010
Energy-preserving Runge-Kutta methods. Zbl 1169.65348
Celledoni, 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 1203.35079
McLachlan, Robert; Zhang, Xingyou
21
2009
Linearization-preserving self-adjoint and symplectic integrators. Zbl 1162.65411
McLachlan, R. I.; Quispel, G. R. W.; Tse, P. S. P.
11
2009
On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067
Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D.
10
2009
The structure of a set of vector fields on Poisson manifolds. Zbl 1162.53061
McLachlan, Robert I.
1
2009
Reconsidering trigonometric integrators. Zbl 1178.65142
O’Neale, Dion R. J.; McLachlan, Robert I.
1
2009
Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058
Hairer, E.; McLachlan, R. I.; Razakarivony, A.
20
2008
Explicit volume-preserving splitting methods for linear and quadratic divergence-free vector fields. Zbl 1147.65053
McLachlan, R. I.; Munthe-Kaas, H. Z.; Quispel, G. R. W.; Zanna, A.
7
2008
On multisymplecticity of partitioned Runge-Kutta methods. Zbl 1172.37030
Ryland, Brett N.; McLachlan, Robert I.
7
2008
On the multisymplecticity of partitioned Runge-Kutta and splitting methods. Zbl 1125.65115
Ryland, Brett N.; McLachlan, Robert I.; Frank, Jason
17
2007
\(N\)-particle dynamics of the Euler equations for planar diffeomorphisms. Zbl 1149.37038
McLachlan, Robert I.; Marsland, Stephen
5
2007
A new implementation of symplectic Runge-Kutta methods. Zbl 1145.65111
McLachlan, Robert I.
5
2007
Discrete mechanics and optimal control for image registration. Zbl 1334.94035
McLachlan, Robert I.; Marsland, Stephen
3
2007
Geometric numerical integration of differential equations. Zbl 1092.65055
McLachlan, Robert; Quispel, Reinout
46
2006
Integrators for nonholonomic mechanical systems. Zbl 1104.37043
McLachlan, R.; Perlmutter, M.
31
2006
The Kelvin-Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms. Zbl 1210.37049
McLachlan, Robert I.; Marsland, Stephen R.
2
2006
On symplectic and multisymplectic schemes for the KdV equation. Zbl 1203.65277
Ascher, U. M.; Mclachlan, R. I.
40
2005
The discrete Moser-Veselov algorithm for the free rigid body, revisited. Zbl 1123.70012
McLachlan, Robert I.; Zanna, Antonella
11
2005
Multisymplectic box schemes and the Korteweg-de Vries equation. Zbl 1038.65138
Ascher, Uri M.; McLachlan, Robert I.
64
2004
Energy drift in reversible time integration. Zbl 1064.37063
McLachlan, R. I.; Perlmutter, M.
6
2004
Explicit geometric integration of polynomial vector fields. Zbl 1066.65150
McLachlan, Robert I.; Quispel, G. Reinout W.
5
2004
On the nonlinear stability of symplectic integrators. Zbl 1070.65130
McLachlan, Robert I.; Perlmutter, Matthew; Quispel, G. R. W.
3
2004
Skew-adjoint finite difference methods on nonuniform grids. Zbl 1073.65084
Kitson, Adrian; McLachlan, Robert I.; Robidoux, Nicolas
8
2003
Geometric integration of conservative polynomial ODEs. Zbl 1021.65064
McLachlan, Robert I.; Quispel, G. R. W.
5
2003
Spatial discretization of partial differential equations with integrals. Zbl 1080.65076
McLachlan, Robert I.
5
2003
The algebraic entropy of classical mechanics. Zbl 1062.70035
McLachlan, Robert I.; Ryland, Brett
1
2003
Splitting methods. Zbl 1105.65341
McLachlan, Robert I.; Quispel, G. Reinout W.
222
2002
Families of high-order composition methods. Zbl 1016.65044
McLachlan, Robert I.
10
2002
Conformal Hamiltonian systems. Zbl 1005.53058
McLachlan, Robert; Perlmutter, Matthew
31
2001
What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration. Zbl 0994.65138
McLachlan, Robert I.; Quispel, G. R. W.
17
2001
Six lectures on the geometric integration of ODEs. Zbl 0978.65056
McLachlan, Robert; Quispel, Reinout
16
2001
Antisymmetry, pseudospectral methods, and conservative PDEs. Zbl 0963.65105
McLachlan, Robert I.; Robidoux, Nicolas
6
2000
Numerical integrators that contract volume. Zbl 0951.65139
McLachlan, Robert I.; Quispel, G. R. W.
2
2000
Geometric integration using discrete gradients. Zbl 0933.65143
McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas
177
1999
Approximately preserving symmetries in the numerical integration of ordinary differential equations. Zbl 0939.65139
Iserles, Arieh; McLachlan, Robert; Zanna, Antonella
7
1999
Area preservation in computational fluid dynamics. Zbl 0966.76073
McLachlan, Robert I.
4
1999
Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals. Zbl 1042.37522
McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas
32
1998
Numerical integrators that preserve symmetries and reversing symmetries. Zbl 0912.34015
McLachlan, R. I.; Quispel, G. R. W.; Turner, G. S.
21
1998
Generating functions for dynamical systems with symmetries, integrals, and differential invariants. Zbl 1194.37089
Mclachlan, Robert I.; Quispel, G. R. W.
6
1998
Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation. Zbl 0888.65095
McLachlan, Robert I.; Gray, Stephen K.
6
1997
Hamiltonian finite-dimensional models of baroclinic instability. Zbl 1024.86500
McLachlan, R. I.; Szunyogh, I.; Zeitlin, V.
2
1997
A survey of open problems in symplectic integration. Zbl 0871.65058
McLachlan, Robert I.; Scovel, Clint
23
1996
More on symplectic correctors. Zbl 0872.65060
McLachlan, Robert I.
5
1996
On the numerical integration of ordinary differential equations by symmetric composition methods. Zbl 0821.65048
McLachlan, Robert I.
100
1995
Composition methods in the presence of small parameters. Zbl 0832.65071
McLachlan, Robert I.
24
1995
Equivariant constrained symplectic integration. Zbl 0836.58017
McLachlan, R. I.; Scovel, C.
16
1995
Comment on “Poisson schemes for Hamiltonian systems on Poisson manifolds”. Zbl 0821.58020
McLachlan, R.
4
1995
Symplectic integration of Hamiltonian wave equations. Zbl 0831.65099
McLachlan, Robert
69
1994
Global behavior of the charged isosceles three-body problem. Zbl 0900.70157
Atela, Pau; McLachlan, Robert I.
10
1994
A gallery of constant-negative-curvature surfaces. Zbl 0812.53003
McLachlan, Robert
6
1994
A note on the motion of surfaces. Zbl 0961.53500
McLachlan, Robert I.; Segur, Harvey
4
1994
Explicit Lie-Poisson integration and the Euler equations. Zbl 0972.65509
McLachlan, Robert I.
37
1993
Explicit symplectic splitting methods applied to PDE’s. Zbl 0788.65095
McLachlan, Robert I.
1
1993
The accuracy of symplectic integrators. Zbl 0747.58032
McLachlan, Robert I.; Atela, Pau
63
1992
The boundary layer on a finite flat plate. Zbl 0718.76035
McLachlan, Robert I.
3
1991
A steady separated viscous corner flow. Zbl 0731.76025
McLachlan, Robert
1
1991
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