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The convergence of splitting schemes for solving a system of nonlinear nonstationary Schrödinger type equations. (Russian. English summary) Zbl 0751.65060

The authors prove the convergence of splitting schemes for a system of nonlinear nonstationary Schrödinger equations in discrete norms \(W^ 1_ 2\), \(C^ 1\). In three-dimensional space variables, the stability of the scheme is proved in the norm \(L_ 2\). There are no restrictions on the ratio of the time step to the spatial step.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35K55 Nonlinear parabolic equations
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