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Zbl 0860.65102
Wu, Lixin
Dufort-Frankel-type methods for linear and nonlinear Schrödinger equations. (English)
[J] SIAM J. Numer. Anal. 33, No.4, 1526-1533 (1996). ISSN 0036-1429; ISSN 1095-7170/e

This is a very clear paper which considers the use of the Dufort-Frankel methods for the discretization of nonlinear Schrödinger equations. These methods are explicit and combine the advantages of both the Crank-Nicolson and the Euler schemes. A proof of the uniqueness of the solution of the nonlinear equation is given which also leads to a conservation law. The chosen discretization schemes also have this conservation law which leads to greater reliability. Numerical examples are given.
[B.Burrows (Stafford)]

MSC 2000:: *65N06 Finite difference methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
35J10 Schroedinger operator
35Q55 NLS-like (nonlinear Schroedinger) equations

Keywords: numerical examples; Crank-Nicolson method; Euler method; Dufort-Frankel methods; nonlinear Schrödinger equations

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