Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations

  • Authors:

  • Jialin Hong;Shanshan Jiang;Chun Li

  • Affiliations:

  • State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Acade ...;School of Mathematics Sciences, Peking University, Beijing 100871, PR China;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Acade ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

In this paper, we propose explicit multi-symplectic schemes for Klein-Gordon-Schrodinger equation by concatenating suitable symplectic Runge-Kutta-type methods and symplectic Runge-Kutta-Nystrom-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.