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Finite difference method with cubic spline for solving nonlinear Schrödinger equation. (English) Zbl 1001.65501
Summary: In this paper we solve the nonlinear Schrödinger equation by discretizing the time derivative using the finite difference method and the space derivative using the cubic spline method. We prove that the resulting scheme is unconditionally stable and conserves energy.

65D07 Numerical computation using splines
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