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

✍ Scribed by Tingchun Wang; Tao Nie; Luming Zhang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
839 KB
Volume
231
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 initialboundary value problem of a coupled nonlinear Schrödinger 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.

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