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Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. (English) Zbl 0806.65123
We examine the use of orthogonal spline collocation for the semidiscretization of the cubic Schrödinger equation and the two- dimensional parabolic equation of F. D. Tappert [The parabolic method. Lect. Notes Physics 70, 224-287 (1977; Zbl 0399.76079)]. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrödinger equation, we present the results of numerical experiments in which the integration in time is performed using a routine from a software library.
MSC:
65Z05Applications of numerical analysis to physics
65M70Spectral, collocation and related methods (IVP of PDE)
65M20Method of lines (IVP of PDE)
65M15Error bounds (IVP of PDE)
35Q55NLS-like (nonlinear Schrödinger) equations