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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.   Google Scholar

[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.   Google Scholar

[3]

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

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[7]

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

[8]

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

[9]

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

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[13]

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

[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.  Google Scholar

[15]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[20]

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

[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.   Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[31]

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

[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.   Google Scholar

[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.   Google Scholar

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.   Google Scholar

[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.   Google Scholar

[3]

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

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[7]

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

[8]

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

[9]

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

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[13]

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

[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.  Google Scholar

[15]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[20]

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

[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.   Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[31]

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

[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.   Google Scholar

[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.   Google Scholar

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