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December  2019, 6(2): i-v. doi: 10.3934/jcd.2019007

Preface Special issue in honor of Reinout Quispel

Elena Celledoni 1, and  Robert I. McLachlan 2,

1. 

Department of Mathematical Sciences, NTNU, Norway
2. 

School of Fundamental Sciences, Massey University, Palmerston North, New Zealand

Published  November 2019

Citation: Elena Celledoni, Robert I. McLachlan. Preface Special issue in honor of Reinout Quispel. Journal of Computational Dynamics, 2019, 6 (2) : i-v. doi: 10.3934/jcd.2019007
References:
[1]

P. Bader, S. Blanes, F. Casas and M. Thalhammer, Efficient time integration methods for Gross-Pitaevskii equations with rotation term, J. Comput. Dyn., 6 (2019), 147-169. 

[2]

M. Benning, E. Celledoni, M. J. Ehrhardt, B. Owren and C.-B. Schönlieb, Deep learning as optimal control problems: Models and numerical methods, J. Comput. Dyn., 6 (2019), 171-198. 

[3]

G. Bogfjellmo, Algebraic structure of aromatic B-series, J. Comput. Dyn., 6 (2019), 199-122. 

[4]

C. J. Budd and A. Iserles, Geometric integration: Numerical solution of differential equations on manifolds, Phil. Trans. Roy. Soc. A Math. Phys. Eng. Sci., 357 (1999), 945-956.  doi: 10.1098/rsta.1999.0360.

[5]

E. Celledoni, R. I. McLachlan, B. Owren and G. R. W. Quispel, Geometric properties of Kahan's method, J. Phys. A, 46 (2012), 025201, 12 pp.  doi: 10.1088/1751-8113/46/2/025201.

[6]

H. Christodoulidi, A. N. W. Hone and T. E. Kouloukas, A new class of integrable Lotka-Volterra systems, J. Comput. Dyn., 6 (2019), 223-237. 

[7]

M. Condon, A. Iserles, K. Kropielnicka and P. Singh, Solving the wave equation with multifrequency oscillations, J. Comput. Dyn., 6 (2019), 239-249. 

[8]

C. Curry, S. Marsland and R. I. McLachlan, Principal symmetric space analysis, J. Comput. Dyn., 6 (2019), 251-276. 

[9]

C. A. Evripidou, P. Kassotakis and P. Vanhaecke, Integrable reductions of the dressing chain, J. Comput. Dyn., 6 (2019), 277-306. 

[10]

G. Frasca-Caccia and P. E. Hydon, Locally conservative finite difference schemes for the modified KdV equation, J. Comput. Dyn., 6 (2019), 307-323. 

[11]

F. A. Haggar, G. B. Byrnes, G. R. W. Quispel and H. W. Capel, K-integrals and k-Lie symmetries in discrete dynamical systems, Physica A, 233 (1996), 379-394. 

[12]

A. Iserles, G. R. W. Quispel and P. S. P. Tse, B-series methods cannot be volume-preserving, BIT Numerical Mathematics, 47 (2007), 351-378.  doi: 10.1007/s10543-006-0114-8.

[13]

N. Joshi and P. Kassotakis, Re-factorising a QRT map, J. Comput. Dyn., 6 (2019), 325-343. 

[14]

J. S. W. Lamb and G. R. W. Quispel, Reversing k-symmetries in dynamical systems, Physica D, 73 (1994), 277-304.  doi: 10.1016/0167-2789(94)90101-5.

[15]

R. I. McLachlan and A. Murua, The Lie algebra of classical mechanics, J. Comput. Dyn., 6 (2019), 345-360. 

[16]

R. I. McLachlan, G. R. W. Quispel and N. Robidoux, Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals, Phys. Rev. Lett., 81 (1998), 2399-2403.  doi: 10.1103/PhysRevLett.81.2399.

[17]

R. I. McLachlan, G. R. W. Quispel and G. S. Turner, Numerical integrators that preserve symmetries and reversing symmetries, SIAM J. Numer. Anal., 35 (1998), 586-599.  doi: 10.1137/S0036142995295807.

[18]

R. I. McLachlan and G. R. W. Quispel, What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration, Nonlinearity, 14 (2001), 1689-1705.  doi: 10.1088/0951-7715/14/6/315.

[19]

Y. Miyatake, T. Nakagawa, T. Sogabe and S.-L. Zhang, A structure-preserving fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation, J. Comput. Dyn., 6 (2019), 361-383. 

[20]

S. Pathiraja and S. Reich, Discrete gradients for computational Bayesian inference, J. Comput. Dyn., 6 (2019), 385-400. 

[21]

M. Petrera and Y. B. Suris, Geometry of the Kahan discretizations of planar quadratic hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor, J. Comput. Dyn., 6 (2019), 401-408. 

[22]

G. R. W. Quispel, Linear Integral Equations and Soliton Systems, thesis, University of Leiden, 1983, https://www.lorentz.leidenuniv.nl/IL-publications/dissertations/sources/Quispel_1983.pdf.

[23]

G. R. W. Quispel and D. I. McLaren, A new class of energy-preserving numerical integration methods, J. Phys. A, 41 (2008), 045206, 7 pp.  doi: 10.1088/1751-8113/41/4/045206.

[24]

G. R. W. Quispel, F. W. Nijhoff, H. W. Capel and J. van der Linden, Linear integral equations and nonlinear difference-difference equations, Physica A: Statistical and Theoretical Physics, 125 (1984), 344-380.  doi: 10.1016/0378-4371(84)90059-1.

[25]

G. R. W. Quispel, J. A. G. Roberts and C. J. Thompson, Integrable mappings and soliton equations. Ⅰ, Phys. Lett. A, 126 (1988), 419-421.  doi: 10.1016/0375-9601(88)90803-1.

[26]

G. R. W. Quispel, J. A. G. Roberts and C. J. Thompson, Integrable mappings and soliton equations Ⅱ, Physica D, 34 (1989), 183-192.  doi: 10.1016/0167-2789(89)90233-9.

[27]

G. R. W. Quispel and H. W. Capel, Solving ODEs numerically while preserving a first integral, Phys. Lett. A, 218 (1996), 223-228.  doi: 10.1016/0375-9601(96)00403-3.

[28]

J. A. G. Roberts and G. R. W. Quispel, Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems, Phys. Rep., 216 (1992), 63-177.  doi: 10.1016/0370-1573(92)90163-T.

[29]

N. Sætran and A. Zanna, Chains of rigid bodies and their numerical simulation by local frame methods, J. Comput. Dyn., 6 (2019), 409-427. 

[30]

Y. Shi, Y. Sun, Y. Wang and J. Liu, Study of adaptive symplectic methods for simulating charged particle dynamics, J. Comput. Dyn., 6 (2019), 429-448. 

[31]

D. T. Tran and J. A. G. Roberts, Linear degree growth in lattice equations, J. Comput. Dyn., 6 (2019), 449-467. 

[32]

J. M. Tuwankotta and E. Harjanto, Strange attractors in a predator-prey system with non-monotonic response function and periodic perturbation, J. Comput. Dyn., 6 (2019), 469-483. 

[33]

M. Zadra and M. L. Mansfield, Using Lie group integrators to solve two dimensional variational problems with symmetry, J. Comput. Dyn., 6 (2019), 485-511. 

show all references

References:
[1]

P. Bader, S. Blanes, F. Casas and M. Thalhammer, Efficient time integration methods for Gross-Pitaevskii equations with rotation term, J. Comput. Dyn., 6 (2019), 147-169. 

[2]

M. Benning, E. Celledoni, M. J. Ehrhardt, B. Owren and C.-B. Schönlieb, Deep learning as optimal control problems: Models and numerical methods, J. Comput. Dyn., 6 (2019), 171-198. 

[3]

G. Bogfjellmo, Algebraic structure of aromatic B-series, J. Comput. Dyn., 6 (2019), 199-122. 

[4]

C. J. Budd and A. Iserles, Geometric integration: Numerical solution of differential equations on manifolds, Phil. Trans. Roy. Soc. A Math. Phys. Eng. Sci., 357 (1999), 945-956.  doi: 10.1098/rsta.1999.0360.

[5]

E. Celledoni, R. I. McLachlan, B. Owren and G. R. W. Quispel, Geometric properties of Kahan's method, J. Phys. A, 46 (2012), 025201, 12 pp.  doi: 10.1088/1751-8113/46/2/025201.

[6]

H. Christodoulidi, A. N. W. Hone and T. E. Kouloukas, A new class of integrable Lotka-Volterra systems, J. Comput. Dyn., 6 (2019), 223-237. 

[7]

M. Condon, A. Iserles, K. Kropielnicka and P. Singh, Solving the wave equation with multifrequency oscillations, J. Comput. Dyn., 6 (2019), 239-249. 

[8]

C. Curry, S. Marsland and R. I. McLachlan, Principal symmetric space analysis, J. Comput. Dyn., 6 (2019), 251-276. 

[9]

C. A. Evripidou, P. Kassotakis and P. Vanhaecke, Integrable reductions of the dressing chain, J. Comput. Dyn., 6 (2019), 277-306. 

[10]

G. Frasca-Caccia and P. E. Hydon, Locally conservative finite difference schemes for the modified KdV equation, J. Comput. Dyn., 6 (2019), 307-323. 

[11]

F. A. Haggar, G. B. Byrnes, G. R. W. Quispel and H. W. Capel, K-integrals and k-Lie symmetries in discrete dynamical systems, Physica A, 233 (1996), 379-394. 

[12]

A. Iserles, G. R. W. Quispel and P. S. P. Tse, B-series methods cannot be volume-preserving, BIT Numerical Mathematics, 47 (2007), 351-378.  doi: 10.1007/s10543-006-0114-8.

[13]

N. Joshi and P. Kassotakis, Re-factorising a QRT map, J. Comput. Dyn., 6 (2019), 325-343. 

[14]

J. S. W. Lamb and G. R. W. Quispel, Reversing k-symmetries in dynamical systems, Physica D, 73 (1994), 277-304.  doi: 10.1016/0167-2789(94)90101-5.

[15]

R. I. McLachlan and A. Murua, The Lie algebra of classical mechanics, J. Comput. Dyn., 6 (2019), 345-360. 

[16]

R. I. McLachlan, G. R. W. Quispel and N. Robidoux, Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals, Phys. Rev. Lett., 81 (1998), 2399-2403.  doi: 10.1103/PhysRevLett.81.2399.

[17]

R. I. McLachlan, G. R. W. Quispel and G. S. Turner, Numerical integrators that preserve symmetries and reversing symmetries, SIAM J. Numer. Anal., 35 (1998), 586-599.  doi: 10.1137/S0036142995295807.

[18]

R. I. McLachlan and G. R. W. Quispel, What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration, Nonlinearity, 14 (2001), 1689-1705.  doi: 10.1088/0951-7715/14/6/315.

[19]

Y. Miyatake, T. Nakagawa, T. Sogabe and S.-L. Zhang, A structure-preserving fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation, J. Comput. Dyn., 6 (2019), 361-383. 

[20]

S. Pathiraja and S. Reich, Discrete gradients for computational Bayesian inference, J. Comput. Dyn., 6 (2019), 385-400. 

[21]

M. Petrera and Y. B. Suris, Geometry of the Kahan discretizations of planar quadratic hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor, J. Comput. Dyn., 6 (2019), 401-408. 

[22]

G. R. W. Quispel, Linear Integral Equations and Soliton Systems, thesis, University of Leiden, 1983, https://www.lorentz.leidenuniv.nl/IL-publications/dissertations/sources/Quispel_1983.pdf.

[23]

G. R. W. Quispel and D. I. McLaren, A new class of energy-preserving numerical integration methods, J. Phys. A, 41 (2008), 045206, 7 pp.  doi: 10.1088/1751-8113/41/4/045206.

[24]

G. R. W. Quispel, F. W. Nijhoff, H. W. Capel and J. van der Linden, Linear integral equations and nonlinear difference-difference equations, Physica A: Statistical and Theoretical Physics, 125 (1984), 344-380.  doi: 10.1016/0378-4371(84)90059-1.

[25]

G. R. W. Quispel, J. A. G. Roberts and C. J. Thompson, Integrable mappings and soliton equations. Ⅰ, Phys. Lett. A, 126 (1988), 419-421.  doi: 10.1016/0375-9601(88)90803-1.

[26]

G. R. W. Quispel, J. A. G. Roberts and C. J. Thompson, Integrable mappings and soliton equations Ⅱ, Physica D, 34 (1989), 183-192.  doi: 10.1016/0167-2789(89)90233-9.

[27]

G. R. W. Quispel and H. W. Capel, Solving ODEs numerically while preserving a first integral, Phys. Lett. A, 218 (1996), 223-228.  doi: 10.1016/0375-9601(96)00403-3.

[28]

J. A. G. Roberts and G. R. W. Quispel, Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems, Phys. Rep., 216 (1992), 63-177.  doi: 10.1016/0370-1573(92)90163-T.

[29]

N. Sætran and A. Zanna, Chains of rigid bodies and their numerical simulation by local frame methods, J. Comput. Dyn., 6 (2019), 409-427. 

[30]

Y. Shi, Y. Sun, Y. Wang and J. Liu, Study of adaptive symplectic methods for simulating charged particle dynamics, J. Comput. Dyn., 6 (2019), 429-448. 

[31]

D. T. Tran and J. A. G. Roberts, Linear degree growth in lattice equations, J. Comput. Dyn., 6 (2019), 449-467. 

[32]

J. M. Tuwankotta and E. Harjanto, Strange attractors in a predator-prey system with non-monotonic response function and periodic perturbation, J. Comput. Dyn., 6 (2019), 469-483. 

[33]

M. Zadra and M. L. Mansfield, Using Lie group integrators to solve two dimensional variational problems with symmetry, J. Comput. Dyn., 6 (2019), 485-511. 

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