Science, Technology and Engineering

Department of Mathematics and Statistics

Mathematics Staff Members

Research Interests

My main research interests are in geometric numerical integration, dynamical systems, and integrable systems.

Other current members of the research group in scientific computation and dynamical systems are David McLaren, Will Wright, Peter van der Kamp, Omar Rojas, and Ivanky Saputra.

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

Publications

1. G.R.W. Quispel and H.W. Capel, 'Equation of Motion for the Heisenberg Spin Chain', Phys. Lett. 85A (1981) 248-250. PDF File
2. G.R.W. Quispel and H.W. Capel, 'Equation of Motion for the Heisenberg Spin Chain', Physica 110A (1982) 41-80. PDF File
3. G.R.W. Quispel and H.W. Capel, 'The Nonlinear Schrödinger Equation and the Anisotropic Heisenberg Spin Chain', Phys. Lett. 88A (1982) 371-374. PDF File
4. F.W. Nijhoff, J. van der Linden, G.R.W. Quispel and H.W. Capel, 'Linearization of the Nonlinear Schrödinger Equation and the Isotropic Heisenberg Spin Chain', Phys. Lett. 89A (1982) 106-108. PDF File
5. F.W. Nijhoff, J. van der Linden, G.R.W. Quispel, H.W. Capel and J. Velthuizen, 'Linearization of the Nonlinear Schrödinger Equation and the Isotropic Heisenberg Spin Chain', Physica 116A (1982) 1-33. PDF File
6. G.R.W. Quispel, F.W. Nijhoff and H.W. Capel, 'Linearization of the Boussinesq Equation and the Modified Boussinesq Equation, Phys. Lett. 91A (1982) 143-145. PDF File
7. G.R.W. Quispel and H.W. Capel, 'The Anisotropic Heisenberg Spin Chain and the Nonlinear Schrödinger Equation', Physica 117A (1983) 76-102. PDF File
8. F.W. Nijhoff, H.W. Capel, G.R.W. Quispel and J. van der Linden, 'The Derivative Nonlinear Schrödinger Equation and the Massive Thirring Model', Phys. Lett. 93A (1983) 455-458. PDF File
9. F.W. Nijhoff, G.R.W. Quispel, J. van der Linden and H.W. Capel, 'On Some Linear Integral Equations Generating Solutions of Nonlinear Partial Differential Equations', Physica 119A (1983) 101-142. PDF File
10. F.W. Nijhoff, G.R.W. Quispel and H.W. Capel, 'Linearization of Nonlinear Differential-Difference Equations', Phys. Lett. 95A (1983) 273-276. PDF File
11. F.W. Nijhoff, G.R.W. Quispel and H.W. Capel, 'Linearization of Nonlinear Difference-Difference Equations', Phys. Lett. 97A (1983) 125-128. PDF File
12. F.W. Nijhoff, H.W. Capel and G.R.W. Quispel, 'Integrable Lattice Version of the Massive Thirring Model and its Linearization', Phys. Lett. 98A (1983) 83-86. PDF File
13. G.R.W. Quispel, 'Linear Integral Equations and Soliton Systems', Thesis, University of Leiden, Department of Theoretical Physics, 1983. PDF File
14. J.H.H. Perk, H.W. Capel, G.R.W. Quispel and F.W. Nijhoff, 'Finite-Temperature Correlations for the Ising Chain in a Transverse Field', Physica 123A (1984) 1-49. PDF File
15. G.R.W. Quispel, F.W. Nijhoff, H.W. Capel and J. van der Linden, 'Backlund Transformations and Singular Integral Equations', Physica 123A (1984) 319-359. PDF File
16. G.R.W. Quispel, F.W. Nijhoff, H.W. Capel and J.van der Linden, 'Linear Integral Equations and Nonlinear Difference-Difference Equations', Physica 125A (1984) 344-380. PDF File
17. F.W. Nijhoff, H.W. Capel, G.L. Wiersma and G.R.W. Quispel, 'Linearizing Integral Transform and Partial Difference Equations', Phys. Lett. 103A (1984) 293-297. PDF File
18. F.W. Nijhoff, H.W. Capel, G.L. Wiersma and G.R.W. Quispel, 'Backlund Transformations and 3-Dimensional Lattice Equations', Phys. Lett. 105A (1984) 267-272. PDF File
19. J.B.J. van Zeijts, G.R.W. Quispel, T.P. Valkering and R.H.G. Helleman, 'Van Mechanische Banen naar Toevalsprocessen, Chaos en Turbulentie', Ned. Tijdschr. voor Natuurk. A50 (1984) 90-95 (in Dutch). PDF File
20. G.R.W. Quispel, 'Analytical Crossover Results for the Feigenbaum Constants: Crossover from Conservative to Dissipative Systems', Phys. Rev. 31A (1985) 3924-3928. PDF File
21. G.R.W. Quispel, 'Scaling of the "Superstable" Fraction of the 2-D Period-Doubling Interval', Phys. Lett. 112A (1985) 353-356. PDF File
22. J.van der Linden, F.W. Nijhoff, H.W. Capel and G.R.W. Quispel, 'Linear Integral Equations and Multicomponent Nonlinear Integrable Systems', Physica 137A (1986) 44-80. PDF File
23. G.R.W. Quispel, 'Analytical Renormalization Results for the Crossover Behaviour of Period-Doubling, from Conservative to Dissipative Systems', Physica 18D (1986) 477-478. PDF File
24. G.R.W. Quispel, 'Universal Functional Equation for Period-Doubling in Constant-Jacobian Maps', Phys. Lett. 118A (1986) 457-462. PDF File
25. C.J. Hamer, G.R.W. Quispel and M.T. Batchelor, 'Conformal Anomaly and Surface Energy for Potts and Ashkin-Teller Quantum Chains', J. Phys. A20 (1987) 5677-5693. PDF File
26. F.C. Alcaraz, M.N. Barber, M.T. Batchelor, R.J. Baxter and G.R.W. Quispel, 'Surface Exponents of the Quantum XXZ, Ashkin-Teller and Potts Models', J. Phys. A20 (1987) 6397-6409. PDF File
27. G.R.W. Quispel, 'The Anisotropic Heisenberg Spin Chain and the Derivative Non-Linear Schrödinger Equation', J. Phys. A20 (1987)L1069-L1070. PDF File
28. G.R.W. Quispel, J.A.G. Roberts and C.J. Thompson, 'Integrable Mappings and Soliton Equations I', Phys. Lett. 126A (1988) 419-421. PDF File
29. G.R.W. Quispel and J.A.G. Roberts, 'Reversible Mappings of the Plane', Phys. Lett. 132A (1988) 161-163. PDF File
30. G.R.W. Quispel and J.A.G. Roberts, 'Conservative and Dissipative Behaviour in Reversible Dynamical Systems', Phys. Lett. 135A (1989) 337-342. PDF File
31. G.R.W. Quispel, J.A.G. Roberts and C.J. Thompson, 'Integrable Mappings and Soliton Equations II', Physica 34D (1989) 183-192. PDF File
32. G.R.W. Quispel and H.W. Capel, 'Local Reversibility in Dynamical Systems', Phys. Lett. 142A (1989) 112-116. PDF File
33. R.J. Baxter and G.R.W. Quispel, 'Hamiltonian limit of the three-dimensional Zamolodchikov model', J. Stat. Phys. 58 (1990) 411-430. PDF File
34. T. Post, H.W. Capel, G.R.W. Quispel and J.P. van der Weele, 'Bifurcations in two-dimensional reversible maps', Physica 164A (1990) 625-662. PDF File
35. G.R.W. Quispel, H.W. Capel, V.G. Papageorgiou and F.W. Nijhoff, 'Integrable Mappings Derived from Soliton Equations', Physica 173A (1991) 243-266. PDF File
36. K.M. Briggs, G.R.W. Quispel and C.J. Thompson, 'Feigenvalues for Mandelsets', J. Phys. A24 (1991) 3363-3368. PDF File
37. J.A.G. Roberts, T. Post, H.W. Capel and G.R.W. Quispel, 'Conservative versus Reversible Dynamical Systems', In Solitons and Chaos, I. Antoniou and F.J. Lambert, Eds. (Springer, Berlin, 1991) 218-226. PDF File
38. H.W. Capel, F.W. Nijhoff, V.G. Papageorgiou and G.R.W. Quispel, 'Integrable Mappings and Soliton Lattices', In Solitons and Chaos, I. Antoniou and F.J. Lambert, Eds. (Springer, Berlin, 1991) 232-239. PDF File
39. G.R.W. Quispel and F.W. Nijhoff, 'Integrable Two-Dimensional Quantum Mappings', Phys. Lett. 161A (1992) 419-422. PDF File
40. J.A.G. Roberts and G.R.W. Quispel, 'Chaos and Time-Reversal Symmetry', Physics Reports 216 (1992) 63-177. PDF File
41. F.W. Nijhoff, V.G. Papageorgiou, H.W. Capel and G.R.W. Quispel, 'The Lattice Gel'fand-Dikii Hierarchy', Inverse Problems 8 (1992) 597-621. PDF File
42. G.R.W. Quispel, H.W. Capel and R. Sahadevan, 'Continuous Symmetries of Differential-Difference Equations', Phys. Lett. 170A (1992) 379-383. PDF File
43. G.R.W. Quispel, 'Chaos and Time-Reversal Symmetry: An Introduction', in Nonlinear Dynamics and Chaos. R.L. Dewar and B.I. Henry, Eds. (World Scientific, Singapore, 1992). PDF File
44. G.R.W. Quispel and R. Sahadevan, 'Continuous Symmetries of Difference Equations', In Modern Group Analysis', N.H.Ibragimov, M.Torrisi and A.Valenti, Eds. (Kluwer, Dordrecht, 1993) 299-302. PDF File
45. G.R.W. Quispel, H.W. Capel and R. Sahadevan, 'Continuous Symmetries and Painlevé Reduction of the Kac-van Moerbeke Equation', In Applications of Analytic and Geometric Methods in Nonlinear Differential Equations, P. Clarkson, Ed. (Kluwer, Dordrecht, 1993) 431-439. PDF File
46. G.R.W. Quispel and M.B. Sevryuk, 'KAM theorems for the product of two involutions of different types', Chaos 3 (1993) 757-769. PDF File
47. G.R.W. Quispel and R. Sahadevan, 'Lie Symmetries and the Integration of Difference Equations', Phys. Lett. 184A (1993) 64-70. PDF File
48. G.S. Turner and G.R.W. Quispel, 'Tupling in Three-Dimensional Reversible Mappings', J. Phys. A, 27 (1994) 757-762. PDF File
49. G.R.W. Quispel and J.S.W. Lamb, 'Dynamics and k-symmetries', Hamiltonian Mechanics: Integrability and Chaotic Behaviour, J. Seimenis, Ed. (New York, Plenum, 1994) 307-314. PDF File
50. J.S.W. Lamb and G.R.W. Quispel, 'Reversing k-symmetries in dynamical systems', Physica 73D (1994) 277-304. PDF File
51. G.B. Byrnes, R. Sahadevan and G.R.W. Quispel, 'Factorizable Lie Symmetries and the Linearization of Difference Equations' Nonlinearity 8 (1995) 443-459. PDF File
52. J.S.W. Lamb and G.R.W. Quispel, 'Cyclic reversing k-symmetry groups', Nonlinearity 8 (1995) 1005-1026. PDF File
53. G.R.W. Quispel, Volume-preserving integrators, Phys. Lett. 206A (1995) 26-30. PDF File
54. G.R.W. Quispel, 'Chaos versus Order in Hamiltonian Dynamical Systems', In Statistical Mechanics and Field Theory' V.V. Bazhanov, and C.J. Burden, Eds. (World Scientific, Singapore, 1995) 307-335 . PDF File
55. G.R.W. Quispel and H.W. Capel, 'Solving ODE's numerically while preserving a first integral', Phys. Lett. 218A (1996) 223-228. PDF File
56. G.R.W. Quispel and G.S. Turner, 'Discrete Gradient Methods for Solving ODE's Numerically while Preserving a First Integral', J. Phys. A29 (1996) L341-349. PDF File
57. G.R.W. Quispel,F.W. Nijhoff and J.H.H.Perk (Eds), 'Statistical Mechanics, Soliton Theory, and Nonlinear Dynamics,', Physica 228A (1996) 1-366. PDF File
58. R. Sahadevan, G.B. Byrnes and G.R.W. Quispel, 'Linearisation of Difference Equations, using Factorizable Lie Symmetries', CRM Proc. and Lecture Notes 9 D. Levi, L. Vinet and P.Winternitz, Eds. (AMS, Providence, R.I., 1996), 337-343. PDF File
59. F. Haggar, G.B. Byrnes, G.R.W. Quispel and H.W. Capel, 'k-integrals and k-Lie symmetries in discrete dynamical systems', Physica 233A (1996) 379-394. PDF File
60. R. Sahadevan and G.R.W. Quispel, 'Lie Symmetries and Linearisation of the QRT mapping, Physica 234A (1997) 775-784. PDF File
61. G.R.W. Quispel and C. Dyt, Solving ODE's Numerically while Preserving Symmetries, Hamiltonian Structure, Phase Space Volume or First Integrals. Proceedings IMALS 1997 World Congress, A.Sydow, Ed., vol. 2, pp 601-607. PDF File
62. R.I. McLachlan, G.R.W. Quispel and G.S. Turner, 'Numerical Integrators that Preserve Symmetries and Reversing Symmetries', SIAM J. Num. Anal. 35 (1998) 586-599. PDF File
63. R.I. McLachlan and G.R.W. Quispel, 'Generating functions for dynamical systems with symmetries, integrals, and differential invariants, Physica 112D (1998) 298-309. PDF File
64. G.R.W. Quispel and C.Dyt, Volume-preserving integrators have linear error growth, Phys. Lett. 242A (1998) 25-30. PDF File
65. R.I.McLachlan, G.R.W. Quispel and N. Robidoux, A unified approach to Hamiltonian systems, Poisson systems, gradient systems and systems with Lyapunov functions and/or first integrals. Phys. Rev. Lett. 81 (1998) 2399-2403. PDF File
66. R.I.McLachlan, G.R.W. Quispel and N. Robidoux, Geometric integration using discrete gradients, Phil. Trans. Roy. Soc. A 357 (1999) 1021-1045. PDF File
67. G.B. Byrnes, F.Haggar and G.R.W. Quispel, Sufficient conditions for dynamical systems to have pre-symplectic or pre-implectic structures, Physica 272A (1999) 99-129. PDF File
68. R.I. McLachlan and G.R.W. Quispel, Numerical integrators that contract volume, Appl. Numer. Math. 34 (2000) 253-260. PDF File
69. G.R.W.Quispel and D.Levi, Discrete Painleve equations from nonisospectral soliton equations, Proceedings of the Third Congress on Symmetry and Integrability of Difference Equations, CRM Proceedings 25 (2000) 363-366. PDF File
70. R.I. McLachlan and G.R.W. Quispel, Six lectures on the geometric integration of ODEs, In "Foundations of Computational Mathematics", C.U.P. (2001), R.A. DeVore et al. eds, 155-210. PDF File
71. H.Z.Munthe-Kaas, G.R.W.Quispel and A.Zanna, Generalized polar decompositions on Lie groups with involutive automorphisms, Foundations of Computational Mathematics 1 (2001) 297-324. PDF File
72. G.R.W.Quispel, H.W.Capel and J.Scully, Piecewise-linear soliton equations and piecewise-linear integrable maps, J.Phys. A34 (2001) 2491-2503. PDF File
73. R.I. McLachlan and G.R.W. Quispel, What kinds of dynamics are there? Nonlinearity 14 (2001) 1689-1705. PDF File
74. J.A.G. Roberts, A. Iatrou and G.R.W. Quispel, Interchanging parameters and integrals in dynamical systems: the mapping case, J. Phys. A35 (2002) 2309-2325. PDF File
75. R.I. McLachlan and G.R.W. Quispel, Splitting methods, Acta Numerica 11 (2002) 341-434. PDF File
76. G.R.W. Quispel, An alternating integrable map whose square is the QRT map, Phys.Lett. 307A (2003) 50-54. PDF File
77. G.R.W. Quispel and D.I. McLaren, Explicit volume-preserving and symplectic integrators for trigonometric polynomial flows, J. Comp. Phys. 186 (2003) 308 - 316. PDF File
78. R.I. McLachlan and G.R.W.Quispel, Geometric integration of conservative polynomial ODEs, Applied Num. Maths. 45 (2003) 411 - 418. PDF File
79. J.M. Tuwankotta and G.R.W.Quispel, Geometric numerical integration applied to the elastic pendulum at higher order resonance, J. Comp. and Appl. Maths. 154 (2003) 229 - 242. PDF File
80. R.I. McLachlan, M. Perlmutter and G.R.W. Quispel, Lie group foliations: dynamical systems and integrators, Future Gen. Comp. Systems, 19 (2003) 1207 - 1219. PDF File
81. R.I. McLachlan, M. Perlmutter and G.R.W. Quispel, On the nonlinear stability of symplectic integrators, BIT 44 (2004) 99 - 117. PDF File
82. D.I. McLaren and G.R.W. Quispel, Integral-preserving integrators, J. Phys. A37 (2004) L489 - L495. PDF File
83. R.I. McLachlan and G.R.W. Quispel, Explicit geometric integration of polynomial vector fields, BIT 44 (2004) 515 - 538. PDF File
84. J.M. Tuwankotta, G.R.W.Quispel and K.M. Tamizhmani, Dynamics and bifurcations of a three-dimensional piecewise-linear integrable map, J. Phys. A37 (2004) 12041 - 12058. PDF File
85. G.R.W. Quispel, H.W. Capel and J.A.G. Roberts, Duality for discrete integrable systems, J. Phys. A38 (2005) 3965-3980. PDF File
86. P. Winternitz, D. Gomez-Ullate, A. Iserles, D. Levi, P.J. Olver, R. Quispel, and P. Tempesta (Editors), Group Theory and Numerical Analysis, CRM Proceedings & Lecture Notes 39, AMS Providence 2005. PDF File
87. E.L. Mansfield and G.R.W Quispel, Towards a variational complex for the finite-element method, in: P. Winternitz, D. Gomez-Ullate, A. Iserles, D. Levi, P.J. Olver, R. Quispel, and P. Tempesta (Editors), Group Theory and Numerical Analysis, CRM Proceedings & Lecture Notes 39, AMS Providence 2005, 207-232. PDF File
88. V. Grimm and G.R.W. Quispel, Geometric Integration Methods that preserve Lyapunov Functions, BIT 45, (2005) 709-723. PDF File
89. G.R.W. Quispel and R.I. McLachlan (eds.), Geometric Numerical Integration of Differential Equations, J. Phys. A39 (2006) 5251-5652. PDF File
90. R.I. Mc Lachlan and G.R.W. Quispel, Geometric Integrators for ODEs, J. Phys. A39 (2006) 5251-5286. PDF File
91. G.R.W.Quispel (joint with D.I.McLaren), Integral-preserving integrators, Oberwolfach Report 14/2006, 844-846. PDF File
92. A.Zanna (joint with R.I.McLachlan, H.Z.Munthe-Kaas and G.R.W.Quispel), Explicit, volume preserving splitting methods for divergence-free polynomial vector fields, Oberwolfach Report 14/2006, 853-854. PDF File
93. J.A.G. Roberts and G.R.W. Quispel, Creating and relating 3-dimensional integrable maps, J. Phys. A39 (2006) L605-L615. PDF File
94. K. Maruno and G.R.W.Quispel, Construction of integrals of higher-order mappings, J. Phys. Soc. Japan 75 (2006) 123001/1-123001/5. PDF File
95. A. Iserles, G.R.W. Quispel and P.S.P. Tse, B-series methods cannot be volume-preserving, BIT 47 (2007), 351-378. PDF File
96. P.H. van der Kamp. O. Rojas and G.R.W. Quispel, Closed-form expressions for integrals of MKdV and sine-Gordon maps, J. Phys. A40 (2007), 12789 - 12798. PDF File
97. O. Rojas, Peter H. van der Kamp and G.R.W. Quispel, Lax representation for integrable OΔEs, proceedings `Symmetry and Perturbation Theory 2007', 271—272. PDF File

98. G.R.W. Quispel and D.I. McLaren, A new class of energy-preserving numerical integration methods, J. Phys. A41 (2008), 045206 (7pp). PDF File

99. V. Grimm and G.R.W. Quispel, Geometric integration methods that unconditionally contract volume, Applied Numerical Mathematics 58 (2008), 1103-1112. PDF File

100. R.I. McLachlan, H.Z. Munthe-Kaas, G.R.W. Quispel and A. Zanna, Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields, Special Issue Dedicated to Arieh Iserles on the Occasion of His Sixtieth Birthday, Foundations of Computational Mathematics 8 (2008), pp. 335-355. PDF File

101. R.I. McLachlan, H.Z. Munthe-Kaas, G.R.W. Quispel and A. Zanna, Guest Editors, Special Issues Dedicated to Arieh Iserles on the Occasion of His Sixtieth Birthday, Foundations of Computational Mathematics 8 (2008) 287-532. Guest Editor's Preface; Table of Contents; FoCM website

To be Published

1. G.R.W. Quispel and H.W. Capel, 'Solving ODE's Numerically while Preserving All First Integrals', submitted for publication. PDF File
2. H. Munthe-Kaas, G.R.W. Quispel, and A.Zanna, Applications of symmetric spaces and Lie triple systems in numerical analysis, preprint.
3. D.I McLaren and G.R.W. Quispel, Bootstrapping discrete-gradient integral-preserving integrators to fourth order, submitted for publication. PDF File

Internal Publications

1. G.R.W. Quispel, 'An Introduction to Conformal Invariance'. Lectures presented at the 1988 ANU Theoretical Physics Summer School on Statistical Mechanics
2. G.R.W. Quispel, 'Order and Chaos in Conservative and in Reversible Systems', Lectures presented at the 1988 Winter School on Theoretical Physics at James Cook University of Northern Queensland. Published as a Report of the Department of Physics, James Cook University.