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Efficient time integration methods for Gross-Pitaevskii equations with rotation term
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Preface Special issue in honor of Reinout Quispel
1. | Department of Mathematical Sciences, NTNU, Norway |
2. | School of Fundamental Sciences, Massey University, Palmerston North, New Zealand |
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. |
[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. 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. |
[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. |
[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. |
[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. 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. |
[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. 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. |
[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. 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. |
[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. |
[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. |
[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. 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. |
[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. 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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