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Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. (English) Zbl 0911.65095
The authors present the use of orthogonal spline collocation methods with C 1 piecewise polynomials of arbitrary degree r3 in each space variable for the spatial discretization of the Schrödinger equation. Various properties of the method are explained, and several lemmas and a number of theorems for the theoretical foundation are given. There are no examples for illustration.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35Q55NLS-like (nonlinear Schrödinger) equations