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A conservative numerical scheme for initial and boundary value problem of nonlinear Schrödinger equation. (Chinese. English summary) Zbl 0961.65081

Summary: A new conservative finite difference scheme is proposed for the nonlinear Schrödinger equation, and its convergence and stability are proved. Numerical examples show that the new difference scheme is better than the scheme proposed by F. Zhang, V. M. Perez-Garcia and L. Vazquez [Appl. Math. Comput. 71, No. 2-3, 165-177 (1995; Zbl 0832.65136)] in precision, when the suitable parameter is adopted.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)

Citations:

Zbl 0832.65136
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