Reinout Quispel

La Trobe Co-author Network

Current members of our research group in scientific computation and integrable systems are David McLaren and Peter van der Kamp.

Former members of our research group include Volker Grimm, Per Christian Moan, Lennaert van Veen, Priscilla Tse, Jitse Niesen, Graham Byrnes, Ramajayam Sahadevan, Chris Dyt, Kie Van Ivanky Saputra, Dion O'Neale, Omar Rojas, Will Wright, Sarah Lobb, Richard Norton, Chris Ormerod, Theodoros Kouloukas, Philipp Bader, Dinh Tran and Charalambos Evripidou.

I was chief investigator of the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, which had a major node at La Trobe University.

Positions

Mathematics and Statistics , School of Engineering and Mathematical Sciences

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selected publications

academic article
- Celledoni EMcLaren DIOwren BQuispel GRW. Geometric and integrability properties of Kahan’s method: The preservation of certain quadratic integrals. Journal of Physics A: Mathematical and Theoretical. 52. 2019
- Van Der Kamp PHCelledoni EMcLachlan RIMcLaren DIOwren BQuispel GRW. Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation. Journal of Physics A: Mathematical and Theoretical. 52. 2019
- Evripidou CAQuispel GRWRoberts JAG. Poisson structures for difference equations. Journal of Physics A: Mathematical and Theoretical. 51. 2018
- Van Der Kamp PHQuispel GRWZhang D-J. Duality for discrete integrable systems II. Journal of Physics A: Mathematical and Theoretical. 51:1-13. 2018
- Hamad KHone ANWVan Der Kamp PQuispel G. QRT maps and related Laurent systems. Advances in Applied Mathematics. 96:216-248. 2018
- Hone ANWKouloukas TEQuispel GRW. Some integrable maps and their Hirota bilinear forms. Journal of Physics A: Mathematical and Theoretical. 51:1-30. 2018
- Grimm VMcLachlan RIMcLaren DIQuispel GSchönlieb C-B. Discrete gradient methods for solving variational image regularisation models. Journal of Physics A: Mathematical and Theoretical. 50. 2017
- Kouloukas TEQuispel GRWVanhaecke P. Liouville integrability and superintegrability of a generalized Lotka–Volterra system and its Kahan discretization. Journal of Physics A: Mathematical and Theoretical. 49:225201-225201. 2016
- van der Kamp PHQuispel GRWTran DT. Poisson brackets of mappings obtained as (q,-p) reductions of lattice equations. Regular and Chaotic Dynamics. 21:682-696. 2016
- McDonald FMcLachlan RIMoore BEQuispel GRW. Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations. Journal of Difference Equations and Applications. 22:913-940. 2016
- Bader PMcLaren DIQuispel GRWWebb M. Volume preservation by Runge-Kutta methods. Applied Numerical Mathematics. 109:123-137. 2016
- Celledoni EMcLachlan RIMcLaren DIOwren BQuispel GRW. Discretization of polynomial vector fields by polarization. Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences. 471. 2015
- Norton RAMcLaren DIQuispel GRWStern AZanna A. PROJECTION METHODS AND DISCRETE GRADIENT METHODS FOR PRESERVING FIRST INTEGRALS OF ODES. Discrete and Continuous Dynamical Systems Series A. 35:2079-2098. 2015
- van der Kamp PHKouloukas TEQuispel GRWTran DTVanhaecke P. Integrable and superintegrable systems associated with multi-sums of products. Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences. 470:1-23. 2014
- Munthe-Kaas HZQuispel GRWZanna A. Symmetric spaces and Lie triple systems in numerical analysis of differential equations. BIT Numerical Mathematics. 54:257-282. 2014
- Norton RAQuispel GRW. Discrete gradient methods for preserving a first integral of an ordinary differential equation.. Discrete and Continuous Dynamical Systems Series A. 34:1147-1170. 2014
- McLachlan RIQuispel GRW. Discrete gradient methods have an energy conservation law.. Discrete and Continuous Dynamical Systems Series A. 34:1099-1104. 2014
- Celledoni EMcLachlan RIMcLaren DIOwren BQuispel GRW. Integrability properties of Kahan's method. Journal of Physics A: Mathematical and Theoretical. 47:1-20. 2014
- Ormerod CMvan der Kamp PHHietarinta JQuispel GRW. Twisted reductions of integrable lattice equations, and their Lax representations. Nonlinearity. 27:1367-1390. 2014
- Van Der Kamp PHBridgman THereman WQuispel GRWvan der Kamp PH. Symbolic Computation of Lax Pairs of Partial Difference Equations using Consistency Around the Cube. Foundations of Computational Mathematics. 13:517-544. 2013
- Hone ANWvan der Kamp PHQuispel GRWTran DT. Integrability of reductions of the discrete Korteweg-de Vries and potential Korteweg-de Vries equations. Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences. 469:20120747-20120747. 2013
- Ormerod CMvan der Kamp PHQuispel GRW. Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations. Journal of Physics A: Mathematical and Theoretical. 46:095204-095204. 2013
- Celledoni EMcLachlan RIOwren BQuispel GRW. Geometric properties of Kahan's method. Journal of Physics A: Mathematical and Theoretical. 46:025201-025201. 2013
- Celledoni EGrimm VMcLachlan RIMcLaren DIO’Neale DOwren BQuispel GRW. Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Journal of Computational Physics. 231:6770-6789. 2012
- Demskoi DKTran DTvan der Kamp PHQuispel GRW. A novel n th order difference equation that may be integrable. Journal of Physics A: Mathematical and Theoretical. 45:135202-135202. 2012
- Van Der Kamp PHTran DTKamp PHVDQuispel GRW. Involutivity of integrals of sine-Gordon, modified KdV and potential KdV maps. Journal of Physics A: Mathematical and Theoretical. 44:295206-295206. 2011
- Celledoni EMcLachlan RIOwren BQuispel GRW. Energy-Preserving Integrators and the Structure of B-series. Foundations of Computational Mathematics. 10:673-693. 2010
- Celledoni EMcLachlan RIOwren BQuispel GRW. On conjugate B-series and their geometric structure. Journal of Numerical Analysis, Industrial and Applied Mathematics. 5:85-94. 2010
- van der Kamp PHQuispel GRW. The staircase method: integrals for periodic reductions of integrable lattice equations. Journal of Physics A: Mathematical and Theoretical. 43:465207-465207. 2010
- Tran DTvan der Kamp PHQuispel GRW. Sufficient number of integrals for the p th-order Lyness equation. Journal of Physics A: Mathematical and Theoretical. 43:302001-302001. 2010
- Saputra KVIQuispel GRWvan Veen L. An integrating factor matrix method to find first integrals. Journal of Physics A: Mathematical and Theoretical. 43:225207-225207. 2010
- Saputra KVeen LQuispel G. The saddle-node-transcritical bifurcation in a population model with constant rate harvesting. Discrete and Continuous Dynamical Systems Series B: a journal bridging mathematics and sciences. 14:233-250. 2010
- Lobb SBNijhoff FWQuispel GRW. Lagrangian multiform structure for the lattice KP system. Journal of Physics A: Mathematical and Theoretical. 42:472002-472002. 2009
- Quispel GRCelledoni EMcLachlan RIMcLaren DIOwren BReinout W. Quispel GWright WM. Energy-preserving Runge-Kutta methods. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). 43:645-649. 2009
- Tran DTvan der Kamp PHQuispel GRW. Closed-form expressions for integrals of traveling wave reductions of integrable lattice equations. Journal of Physics A: Mathematical and Theoretical. 42:225201-225201. 2009
- McLachlan RIQuispel GRWTse PSP. Linearization-preserving self-adjoint and symplectic integrators. BIT Numerical Mathematics. 49:177-197. 2009
- Grimm VQuispel GRW. Geometric integration methods that unconditionally contract volume. Applied Numerical Mathematics. 58:1103-1112. 2008
- McLachlan RIMunthe-Kaas HZQuispel GRWZanna A. Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields. Foundations of Computational Mathematics. 8:335-355. 2008
- Quispel GRWMcLaren DI. A new class of energy-preserving numerical integration methods. Journal of Physics A: Mathematical and Theoretical. 41:045206-045206. 2008
- van der Kamp PHRojas OQuispel GRW. Closed-form expressions for integrals of MKdV and sine-Gordon maps. Journal of Physics A: Mathematical and Theoretical. 40:12789-12798. 2007
- Iserles AQuispel GRWTse PSP. B-SERIES METHODS CANNOT BE VOLUME-PRESERVING. BIT Numerical Mathematics. 47:351-378. 2007
- Quispel GRMaruno K-IReinout W. Quispel G. Construction of Integrals of Higher-Order Mappings. Journal of the Physical Society of Japan. 75:123001-123001. 2006
- Roberts JAGQuispel GRW. Creating and relating three-dimensional integrable maps. Journal of Physics A: Mathematical and Theoretical. 39:L605-L615. 2006
- Quispel RMcLachlan R. Geometric Numerical Integration of Differential Equations. Journal of Physics A: Mathematical and Theoretical. 39:1. 2006
- McLachlan RIQuispel GRW. Geometric integrators for ODEs. Journal of Physics A: Mathematical and Theoretical. 39:5251-5285. 2006
- Quispel GRWCapel HWRoberts JAG. Duality for discrete integrable systems. Journal of Physics A: Mathematical and Theoretical. 38:3965-3980. 2005
- Tuwankotta JMQuispel GRWTamizhmani KM. Dynamics and bifurcations of a three-dimensional piecewise-linear integrable map. Journal of Physics A: Mathematical and Theoretical. 37:12041-12058. 2004
- McLaren DIQuispel GRW. Integral-preserving integrators. Journal of Physics A: Mathematical and Theoretical. 37:L489-L495. 2004
- McLachlan RIQuispel GRW. Explicit Geometric Integration of Polynomial Vector Fields. BIT Numerical Mathematics. 44:515-538. 2004
- McLachlan RIPerlmutter MQuispel GRW. On the Nonlinear Stability of Symplectic Integrators. BIT Numerical Mathematics. 44:99-117. 2004
- McLachlan RIQuispel GRW. Geometric integration of conservative polynomial ODEs. Applied Numerical Mathematics. 45:411-418. 2003
- Tuwankotta JMQuispel GRW. Geometric numerical integration applied to the elastic pendulum at higher-order resonance. Journal of Computational and Applied Mathematics. 154:229-242. 2003
- Quispel GRWMcLaren DI. Explicit volume-preserving and symplectic integrators for trigonometric polynomial flows. Journal of Computational Physics. 186:308-316. 2003
- Quispel GRW. An alternating integrable map whose square is the QRT map. Physics Letters Section A: General, Atomic and Solid State Physics. 307:50-54. 2003
- Roberts JAGIatrou AQuispel GRW. Interchanging parameters and integrals in dynamical systems: the mapping case. Journal of Physics A: Mathematical and Theoretical. 35:2309-2325. 2002
- McLachlan RIQuispel GRW. Splitting methods. Acta Numerica. 11:341-434. 2002
- McLachlan RIQuispel GRW. What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration. Nonlinearity. 14:1689-1705. 2001
- Munthe-Kaas HZQuispel GRWZanna A. Generalized Polar Decompositions on Lie Groups with Involutive Automorphisms. Foundations of Computational Mathematics. 1:297-324. 2001
- Quispel GRWCapel HWScully J. Piecewise-linear soliton equations and piecewise-linear integrable maps. Journal of Physics A: Mathematical and Theoretical. 34:2491-2503. 2001
- McLachlan RIQuispel GRW. Numerical integrators that contract volume. Applied Numerical Mathematics. 34:253-260. 2000
- Quispel GLevi D. Discrete Painlevé equations from nonisospectral soliton equations.. Centre de recherches mathématiques proceedings & lecture notes. 25:363-366. 2000
- Byrnes GBHaggar FAQuispel GRW. Sufficient conditions for dynamical systems to have pre-symplectic or pre-implectic structures. Physica A: Statistical Mechanics and its Applications. 272:99-129. 1999
- McLachlan RIQuispel GRWRobidoux N. Geometric integration using discrete gradients. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 357:1021-1045. 1999
- McLachlan RIQuispel GRWRobidoux N. Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals. Physical Review Letters. 81:2399-2403. 1998
- Quispel GRDyt C. Volume-preserving integrators have linear error growth. Physics Letters Section A: General, Atomic and Solid State Physics. 242:25-30. 1998
- McLachlan RIQuispel GRWTurner GS. Numerical Integrators that Preserve Symmetries and Reversing Symmetries. SIAM Journal on Numerical Analysis. 35:586-599. 1998
- McLachlan RIQuispel GRW. Generating functions for dynamical systems with symmetries, integrals, and differential invariants. Physica D: Nonlinear Phenomena. 112:298-309. 1998
- Sahadevan RQuispel GRW. Lie symmetries and linearisation of the QRT mapping. Physica A: Statistical Mechanics and its Applications. 234:775-784. 1997
- Haggar FAByrnes GBQuispel GRWCapel HW. k-integrals and k-Lie symmetries in discrete dynamical systems. Physica A: Statistical Mechanics and its Applications. 233:379-394. 1996
- Quispel GRWCapel HW. Solving ODEs numerically while preserving a first integral. Physics Letters Section A: General, Atomic and Solid State Physics. 218:223-228. 1996
- Quispel GRWTurner GS. Discrete gradient methods for solving ODEs numerically while preserving a first integral. Journal of Physics A: Mathematical and Theoretical. 29:L341-L349. 1996
- Lamb JSWQuispel GRW. Cyclic reversing k-symmetry groups. Nonlinearity. 8:1005-1026. 1995
- Quispel GRWuispel GRW. Volume-preserving integrators. Physics Letters Section A: General, Atomic and Solid State Physics. 206:26-30. 1995
- Byrnes GBSahadevan RQuispel GRW. Factorizable Lie symmetries and the linearization of difference equations. Nonlinearity. 8:443-459. 1995
- Lamb JSWQuispel GRW. Reversing k-symmetries in dynamical systems. Physica D: Nonlinear Phenomena. 73:277-304. 1994
- Turner GSQuispel GRW. Tupling in three-dimensional reversible mappings. Journal of Physics A: Mathematical and Theoretical. 27:757-762. 1994
- Quispel GRWSahadevan R. Lie symmetries and the integration of difference equations. Physics Letters Section A: General, Atomic and Solid State Physics. 184:64-70. 1993
- Quispel GRWSevryuk MB. KAM theorems for the product of two involutions of different types. Chaos. 3:757-769. 1993
- Quispel GRWCapel HWSahadevan R. Continuous symmetries of differential-difference equations: the Kac-van Moerbeke equation and Painlevé reduction. Physics Letters Section A: General, Atomic and Solid State Physics. 170:379-383. 1992
- Nijhoff FWPapageorgiou VGCapel HWQuispel GRW. The lattice Gel'fand-Dikii hierarchy. Inverse Problems. 8:597-621. 1992
- Quispel GRRoberts J. Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems. Physics Reports. 216:63-177. 1992
- Quispel GRWNijhoff FW. Integrable two-dimensional quantum mappings. Physics Letters Section A: General, Atomic and Solid State Physics. 161:419-422. 1992
- Briggs KMQuispel GRWThompson CJ. Feigenvalues for Mandelsets. Journal of Physics A: Mathematical and Theoretical. 24:3363-3368. 1991
- Quispel GRWCapel HWPapageorgiou VGNijhoff FW. Integrable mappings derived from soliton equations. Physica A: Statistical Mechanics and its Applications. 173:243-266. 1991
- Post TCapel HWQuispel GRWVan Der Weele JP. Bifurcations in two-dimensional reversible maps. Physica A: Statistical Mechanics and its Applications. 164:625-662. 1990
- Baxter RJQuispel GRW. Hamiltonian limit of the 3D Zamolodchikov model. Journal of Statistical Physics. 58:411-430. 1990
- Quispel GRWCapel HW. Local reversibility in dynamical systems. Physics Letters Section A: General, Atomic and Solid State Physics. 142:112-116. 1989
- Quispel GRWRoberts JAG. Conservative and dissipative behaviour in reversible dynamical systems. Physics Letters Section A: General, Atomic and Solid State Physics. 135:337-342. 1989
- Quispel GRWRoberts JAGThompson CJ. Integrable mappings and soliton equations II. Physica D: Nonlinear Phenomena. 34:183-192. 1989
- Quispel GRWRoberts JAG. Reversible mappings of the plane. Physics Letters Section A: General, Atomic and Solid State Physics. 132:161-163. 1988
- Quispel GRWRoberts JAGThompson CJ. Integrable mappings and soliton equations. Physics Letters Section A: General, Atomic and Solid State Physics. 126:419-421. 1988
- Alcaraz FCBarber MNBatchelor MTBaxter RJQuispel GRW. Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models. Journal of Physics A: Mathematical and Theoretical. 20:6397-6409. 1987
- Hamer CJQuispel GRWBatchelor MT. Conformal anomaly and surface energy for Potts and Ashkin-Teller quantum chains. Journal of Physics A: Mathematical and Theoretical. 20:5677-5693. 1987
- Quispel GRW. The anisotropic Heisenberg spin chain and the derivative nonlinear Schrodinger equation. Journal of Physics A: Mathematical and Theoretical. 20:L1069-L1070. 1987
- Quispel GRW. Universal functional equation for period doubling in constant-Jacobian maps. Physics Letters Section A: General, Atomic and Solid State Physics. 118:457-462. 1986
- van der Linden JNijhoff FWCapel HWQuispel GRW. Linear integral equations and multicomponent nonlinear integrable systems I. Physica A: Statistical Mechanics and its Applications. 137:44-80. 1986
- Quispel GRW. Scaling of the “superstable” fraction of the 2D period-doubling interval. Physics Letters Section A: General, Atomic and Solid State Physics. 112:353-356. 1985
- Quispel GRW. Analytical crossover results for the Feigenbaum constants: Crossover from conservative to dissipative systems. Physical review. A, General physics. 31:3924-3928. 1985
- Nijhoff FWCapel HWWiersma GLQuispel GRW. Bäcklund transformations and three-dimensional lattice equations. Physics Letters Section A: General, Atomic and Solid State Physics. 105:267-272. 1984
- Quispel GRWNijhoff FWCapel HWVan Der Linden J. Linear integral equations and nonlinear difference-difference equations. Physica A: Statistical Mechanics and its Applications. 125:344-380. 1984
- Nijhoff FWCapel HWWiersma GLQuispel GRW. Linearizing integral transform and partial difference equations. Physics Letters Section A: General, Atomic and Solid State Physics. 103:293-297. 1984
- Quispel GRWNijhoff FWCapel HWder Linden J. Bäklund transformations and singular integral equations. Physica A: Statistical Mechanics and its Applications. 123:319-359. 1984
- Perk JHHCapel HWQuispel GRWNijhoff FW. Finite-temperature correlations for the Ising chain in a transverse field. Physica A: Statistical Mechanics and its Applications. 123:1-49. 1984
- Nijhoff FWCapel HWQuispel GRW. Integrable lattice version of the massive thirring model and its linearization. Physics Letters Section A: General, Atomic and Solid State Physics. 98:83-86. 1983
- Nijhoff FWQuispel GRWCapel HW. Direct linearization of nonlinear difference-difference equations. Physics Letters Section A: General, Atomic and Solid State Physics. 97:125-128. 1983
- Nijhoff FWQuispel GRWCapel HW. Linearization of nonlinear differential—Difference equations. Physics Letters Section A: General, Atomic and Solid State Physics. 95:273-276. 1983
- Nijhoff FWQuispel GRWVan Der Linden JCapel HW. On some linear integral equations generating solutions of nonlinear partial differential equations. Physica A: Statistical Mechanics and its Applications. 119:101-142. 1983
- Nijhoff FWCapel HWQuispel GRWvan der Linden J. The derivative nonlinear Schrödinger equation and the massive Thirring model. Physics Letters Section A: General, Atomic and Solid State Physics. 93:455-458. 1983
- Quispel GRWCapel HW. The Anisotropic Heisenberg spin chain and the nonlinear Schrödinger equation. Physica A: Statistical Mechanics and its Applications. 117:76-102. 1983
- Nijhoff FWVan Der Linden JQuispel GRWCapel HWVelthuizen J. Linearization of the nonlinear Schrödinger equation and the isotropic Heisenberg spin chain. Physica A: Statistical Mechanics and its Applications. 116:1-33. 1982
- Quispel GRWNijhoff FWCapel HW. Linearization of the Boussinesq equation and the modified Boussinesq equation. Physics Letters Section A: General, Atomic and Solid State Physics. 91:143-145. 1982
- Nijhoff FWvan der Linden JQuispel GRWCapel HW. Linearization of the nonlinear schrödinger equation and the isotropic heisenberg spin chain. Physics Letters Section A: General, Atomic and Solid State Physics. 89:106-108. 1982
- Quispel GRWCapel HW. The nonlinear Schrödinger equation and the anisotropic Heisenberg spin chain. Physics Letters Section A: General, Atomic and Solid State Physics. 88:371-374. 1982
- Quispel GRWCapel HW. Equation of motion for the Heisenberg spin chain. Physica A: Statistical Mechanics and its Applications. 110:41-80. 1982
- Quispel GRWCapel HW. Equation of motion for the Heisenberg spin chain. Physics Letters Section A: General, Atomic and Solid State Physics. 85:248-250. 1981
chapter
- McLaren DQuispel G. Bootstrapping discrete-gradient integral-preserving integrators to fourth order. 157-171. 2009
- Maclachlan RQuispel G. Six lectures on the geometric intergration of ODEs.. 155-210. 2001
conference paper
- Iserles AQuispel GRR. Why geometric numerical integration?. Springer Proceedings in Mathematics and Statistics. 1-28. 2018
- Celledoni EMcLachlan RIOwren BQuispel GRW. Structure of B-series for some classes of geometric integrators. AIP Conference Proceedings. 739-742. 2009
- Celledoni EMcLaren DMcLachlan ROwren BQuispel GWright W. Energy-preserving methods and B-series.. 21 Nordic seminar on computational mechanics. 1-4. 2008
- Rojas OVan Der Kamp PQuispel G. Lax representation for integrable ODE's.. 271-272. 2008
- Quispel GRHairer EHochbruck MIserles ALubich C. Geometric Numerical Integration. Oberwolfach Reports. 805-882. 2006
- Quispel GMcLaren D. Integral-preserving integrators.. 844-846. 2006
- Grimm VQuispel GRW. Geometric Integration Methods that Preserve Lyapunov Functions. BIT Numerical Mathematics. 709-723. 2005
- Mansfield ELQuispel GRW. Towards a variational complex for the finite element method. Group Theory and Numerical Analysis. 207-232. 2005
- McLachlan RIPerlmutter MQuispel GRW. Lie group foliations: dynamical systems and integrators. Future Generation Computer Systems: the international journal of grid computing: theory, methods and applications. 1207-1219. 2003
- QUISPEL GRWLAMB JSW. DYNAMICS AND K-SYMMETRIES. Nato Asi Series B Physics. 307-314. 1994
- QUISPEL GRWCAPEL HWSAHADEVAN R. CONTINUOUS SYMMETRIES AND PAINLEVE REDUCTION OF THE KAC-VANMOERBEKE EQUATION. Nato Asi Series C Mathematical and Physical Sciences. 431-439. 1993
- QUISPEL GRWSAHADEVAN R. CONTINUOUS SYMMETRIES OF DIFFERENCE-EQUATIONS. MODERN GROUP ANALYSIS: ADVANCED ANALYTICAL AND COMPUTATIONAL METHODS IN MATHEMATICAL PHYSICS. 299-302. 1993