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A relaxation scheme for the nonlinear Schrödinger equation. (English) Zbl 1077.65103
The author proposes a new numerical scheme for the nonlinear Schrödinger equation. This is a relaxation-type scheme that avoids solving nonlinear systems and preserves density and energy. Convergence results for the semidiscretized version of the scheme are obtained. Numerical examples are also presented.

MSC:
65M20 Method of lines 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)
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