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Zbl 0806.65123
Robinson, Mark P.; Fairweather, Graeme
Orthogonal spline collocation methods for Schrödinger-type equations in one space variable.
(English)
[J] Numer. Math. 68, No.3, 355-375 (1994). ISSN 0029-599X; ISSN 0945-3245/e

We examine the use of orthogonal spline collocation for the semidiscretization of the cubic Schrödinger equation and the two- dimensional parabolic equation of {\it F. D. Tappert} [The parabolic method. Lect. Notes Physics 70, 224-287 (1977; Zbl 0399.76079)]. In each case, an optimal order $L\sp 2$ 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.
[M.P.Robinson (Bowling Green)]
MSC 2000:
*65Z05 Applications to physics
65M70 Spectral, collocation and related methods (IVP of PDE)
65M20 Method of lines (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35Q55 NLS-like (nonlinear Schroedinger) equations

Keywords: error bounds; method of lines; orthogonal spline collocation; semidiscretization; cubic Schrödinger equation; numerical experiments

Citations: Zbl 0399.76079

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