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Dufort-Frankel-type methods for linear and nonlinear Schrödinger equations. (English) Zbl 0860.65102
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.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J10 Schrödinger operator, Schrödinger equation
35Q55 NLS equations (nonlinear Schrödinger equations)
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