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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:
65N06Finite difference methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
35J10Schrödinger operator
35Q55NLS-like (nonlinear Schrödinger) equations