Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations. (English) Zbl 1164.65035
Summary: We propose explicit multi-symplectic schemes for Klein-Gordon-Schrödinger equation by concatenating suitable symplectic Runge-Kutta-type methods and symplectic Runge-Kutta-Nyström-type methods for discretizing every partial derivative in each sub-equation. It is further shown that methods constructed in this way are multi-symplectic and preserve exactly the discrete charge conservation law provided appropriate boundary conditions.
In the aim of the commonly practical applications, a novel 2-order one-parameter family of explicit multi-symplectic schemes through such concatenation is constructed, and the numerous numerical experiments and comparisons are presented to show the efficiency and some advantages of the our newly derived methods. Furthermore, some high-order explicit multi-symplectic schemes of such category are given as well, good performances and efficiencies and some significant advantages for preserving the important invariants are investigated by means of numerical experiments.
In the aim of the commonly practical applications, a novel 2-order one-parameter family of explicit multi-symplectic schemes through such concatenation is constructed, and the numerous numerical experiments and comparisons are presented to show the efficiency and some advantages of the our newly derived methods. Furthermore, some high-order explicit multi-symplectic schemes of such category are given as well, good performances and efficiencies and some significant advantages for preserving the important invariants are investigated by means of numerical experiments.
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
Klein-Gordon-Schrödinger equation; multi-symplectic integrator; Runge-Kutta-Nyström method; Runge-Kutta-type method; explicit methods; numerical experimentsReferences:
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