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A note on the numerical solution of the semilinear Schrödinger equation. (English) Zbl 1239.65053
Summary: The unique solvability of local and nonlocal boundary value problems for the semilinear Schrödinger equation in a Hilbert space is investigated. The convergence estimates for the solution of difference schemes are established. Some numerical examples illustrating the methods described in our work are given. Applicability of these methods to nonlinear Schrödinger equation is discussed.

MSC:
65L12Finite difference methods for ODE (numerical methods)
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References:
[1] M.E. Mayfield, Non-reflective boundary conditions for Schrödinger’s equation, Ph.D. Thesis, University of Rhode Island, 1989
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