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Zbl 0911.65095
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. (English)
[J] SIAM J. Numer. Anal. 35, No.2, 453-477 (1998). ISSN 0036-1429; ISSN 1095-7170/e

The authors present the use of orthogonal spline collocation methods with $C^1$ piecewise polynomials of arbitrary degree $r\ge 3$ 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.
[P.K.Mahanti (Ranchi)]

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35Q55 NLS-like (nonlinear Schroedinger) equations

Keywords: Schrödinger equation; orthogonal spline collocation; Gauss points; Crank-Nicolson scheme; alternating direction implicit method; Sobolev space

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Zentralblatt MATH Berlin [Germany]