Analysis of a symplectic difference scheme for a coupled nonlinear Schrodinger system

作者：Wang Tingchun; Nie Tao^*; Zhang Luming

来源：Journal of Computational and Applied Mathematics, 2009, 231(2): 745-759.

DOI：10.1016/j.cam.2009.04.022

• Coupled nonlinear Schrodinger equations
• Symplectic scheme
• Solvability
• Convergence
• Iterative algorithm

In general, proofs of convergence and stability are difficult for symplectic schemes of nonlinear equations. In this paper, a symplectic difference scheme is proposed for an initial-boundary value problem of a coupled nonlinear Schrodinger system. An important lemma and an induction argument are used to prove the unique solvability, convergence and stability of numerical solutions. An iterative algorithm is also proposed for the symplectic scheme and its convergence is proved. Numerical examples show the efficiency of the symplectic scheme and the correction of our numerical analysis.

• 出版日期2009-9-15
• 单位北京应用物理与计算数学研究所; 南京航空航天大学