Preface. Special issue in honor of Reinout Quispel. (English) Zbl 1489.00025
From the text: The papers in this special issue span a wide range of topics closely related to Reinout’s research interests. There are three papers on continuous dynamical systems, all related to predator-prey equations. There are three papers on discrete integrable systems. The remaining papers concern geometric numerical integration and its applications.
MSC:
| 00B15 | Collections of articles of miscellaneous specific interest |
| 37-06 | Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory |
| 65-06 | Proceedings, conferences, collections, etc. pertaining to numerical analysis |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
Biographic References:
Quispel, ReinoutReferences:
| [1] | P. Bader; S. Blanes; F. Casas; M. Thalhammer, Efficient time integration methods for Gross-Pitaevskii equations with rotation term, J. Comput. Dyn., 6, 147-169 (2019) · Zbl 1434.35175 |
| [2] | M. Benning; E. Celledoni; M. J. Ehrhardt; B. Owren; C.-B. Schönlieb, Deep learning as optimal control problems: Models and numerical methods, J. Comput. Dyn., 6, 171-198 (2019) · Zbl 1429.68249 |
| [3] | G. Bogfjellmo, Algebraic structure of aromatic B-series, J. Comput. Dyn., 6, 199-122 (2019) · Zbl 1434.37045 |
| [4] | C. J. Budd; A. Iserles, Geometric integration: Numerical solution of differential equations on manifolds, Phil. Trans. Roy. Soc. A Math. Phys. Eng. Sci., 357, 945-956 (1999) · Zbl 0933.65142 · doi:10.1098/rsta.1999.0360 |
| [5] | E. Celledoni; R. I. McLachlan; B. Owren; G. R. W. Quispel, Geometric properties of Kahan’s method, J. Phys. A, 46, 025201, 12 pp (2012) · Zbl 1278.65192 · doi:10.1088/1751-8113/46/2/025201 |
| [6] | H. Christodoulidi; A. N. W. Hone; T. E. Kouloukas, A new class of integrable Lotka-Volterra systems, J. Comput. Dyn., 6, 223-237 (2019) · Zbl 1434.37036 |
| [7] | M. Condon; A. Iserles; K. Kropielnicka; P. Singh, Solving the wave equation with multifrequency oscillations, J. Comput. Dyn., 6, 239-249 (2019) · Zbl 1434.65200 |
| [8] | C. Curry; S. Marsland; R. I. McLachlan, Principal symmetric space analysis, J. Comput. Dyn., 6, 251-276 (2019) · Zbl 1437.62217 |
| [9] | C. A. Evripidou; P. Kassotakis; P. Vanhaecke, Integrable reductions of the dressing chain, J. Comput. Dyn., 6, 277-306 (2019) · Zbl 1440.53090 |
| [10] | G. Frasca-Caccia; P. E. Hydon, Locally conservative finite difference schemes for the modified KdV equation, J. Comput. Dyn., 6, 307-323 (2019) · Zbl 1436.65100 |
| [11] | F. A. Haggar; G. B. Byrnes; G. R. W. Quispel; H. W. Capel, K-integrals and k-Lie symmetries in discrete dynamical systems, Physica A, 233, 379-394 (1996) · Zbl 0985.37053 |
| [12] | A. Iserles; G. R. W. Quispel; P. S. P. Tse, B-series methods cannot be volume-preserving, BIT Numerical Mathematics, 47, 351-378 (2007) · Zbl 1128.65054 · doi:10.1007/s10543-006-0114-8 |
| [13] | N. Joshi; P. Kassotakis, Re-factorising a QRT map, J. Comput. Dyn., 6, 325-343 (2019) · Zbl 1434.37039 |
| [14] | J. S. W. Lamb; G. R. W. Quispel, Reversing k-symmetries in dynamical systems, Physica D, 73, 277-304 (1994) · Zbl 0814.58035 · doi:10.1016/0167-2789(94)90101-5 |
| [15] | R. I. McLachlan; A. Murua, The Lie algebra of classical mechanics, J. Comput. Dyn., 6, 345-360 (2019) · Zbl 1431.17004 |
| [16] | R. I. McLachlan; G. R. W. Quispel; N. Robidoux, Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals, Phys. Rev. Lett., 81, 2399-2403 (1998) · Zbl 1042.37522 · doi:10.1103/PhysRevLett.81.2399 |
| [17] | R. I. McLachlan; G. R. W. Quispel; G. S. Turner, Numerical integrators that preserve symmetries and reversing symmetries, SIAM J. Numer. Anal., 35, 586-599 (1998) · Zbl 0912.34015 · doi:10.1137/S0036142995295807 |
| [18] | R. I. McLachlan; G. R. W. Quispel, What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration, Nonlinearity, 14, 1689-1705 (2001) · Zbl 0994.65138 · doi:10.1088/0951-7715/14/6/315 |
| [19] | Y. Miyatake; T. Nakagawa; T. Sogabe; S.-L. Zhang, A structure-preserving fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation, J. Comput. Dyn., 6, 361-383 (2019) · Zbl 1434.65207 |
| [20] | S. Pathiraja; S. Reich, Discrete gradients for computational Bayesian inference, J. Comput. Dyn., 6, 385-400 (2019) · Zbl 1437.62110 |
| [21] | M. Petrera; Y. B. Suris, Geometry of the Kahan discretizations of planar quadratic hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor, J. Comput. Dyn., 6, 401-408 (2019) · Zbl 1457.37085 |
| [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; D. I. McLaren, A new class of energy-preserving numerical integration methods, J. Phys. A, 41, 045206, 7 pp (2008) · Zbl 1132.65065 · doi:10.1088/1751-8113/41/4/045206 |
| [24] | G. R. W. Quispel; F. W. Nijhoff; H. W. Capel; J. van der Linden, Linear integral equations and nonlinear difference-difference equations, Physica A: Statistical and Theoretical Physics, 125, 344-380 (1984) · Zbl 0598.45009 · doi:10.1016/0378-4371(84)90059-1 |
| [25] | G. R. W. Quispel; J. A. G. Roberts; C. J. Thompson, Integrable mappings and soliton equations. Ⅰ, Phys. Lett. A, 126, 419-421 (1988) · Zbl 0679.58023 · doi:10.1016/0375-9601(88)90803-1 |
| [26] | G. R. W. Quispel; J. A. G. Roberts; C. J. Thompson, Integrable mappings and soliton equations Ⅱ, Physica D, 34, 183-192 (1989) · Zbl 0679.58024 · doi:10.1016/0167-2789(89)90233-9 |
| [27] | G. R. W. Quispel; H. W. Capel, Solving ODEs numerically while preserving a first integral, Phys. Lett. A, 218, 223-228 (1996) · Zbl 0972.65507 · doi:10.1016/0375-9601(96)00403-3 |
| [28] | J. A. G. Roberts; G. R. W. Quispel, Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems, Phys. Rep., 216, 63-177 (1992) · doi:10.1016/0370-1573(92)90163-T |
| [29] | N. Sætran; A. Zanna, Chains of rigid bodies and their numerical simulation by local frame methods, J. Comput. Dyn., 6, 409-427 (2019) · Zbl 1431.70005 |
| [30] | Y. Shi; Y. Sun; Y. Wang; J. Liu, Study of adaptive symplectic methods for simulating charged particle dynamics, J. Comput. Dyn., 6, 429-448 (2019) · Zbl 1432.37110 |
| [31] | D. T. Tran; J. A. G. Roberts, Linear degree growth in lattice equations, J. Comput. Dyn., 6, 449-467 (2019) · Zbl 1478.37078 |
| [32] | J. M. Tuwankotta; E. Harjanto, Strange attractors in a predator-prey system with non-monotonic response function and periodic perturbation, J. Comput. Dyn., 6, 469-483 (2019) · Zbl 1434.37052 |
| [33] | M. Zadra; M. L. Mansfield, Using Lie group integrators to solve two dimensional variational problems with symmetry, J. Comput. Dyn., 6, 485-511 (2019) · Zbl 1433.58015 |
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