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On convergence and stability of the explicit difference method for solution of nonlinear Schrödinger equations. (English) Zbl 0944.65112
This paper concerns the first boundary value problem for a nonlinear Schrödinger equation. The conditional convergence and stability on the initial data of the explicit three-level difference scheme of DuFort-Frankel type in $$C$$ and $$W^1_2$$ norms are proved. Grid analogues of energy conservation laws and grid multiplicative inequalities are used.

##### MSC:
 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N06 Finite difference methods for boundary value problems involving PDEs 35Q55 NLS equations (nonlinear Schrödinger equations)
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