A dissipative exponentially-fitted method for the numerical solution of the Schrodinger equation and related problems

In this paper a dissipative exponentially-fitted method for the numerical integration of the Schrodinger equation and related problems is developed. The method is called dissipative since is a nonsymmetric multistep method. An application to the the resonance problem of the radial Schrodinger equation and to other well known related problems indicates that the new method is more efficient than the corresponding classical dissipative method and other well known methods. Based on the new method and the method of Raptis and Cash a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schrodinger equation indicates the power of the new approach. (C) 2003 Published by Elsevier Science B.V.