Effective Numerical Approximation of Schrödinger type Equations through Multiderivative Exponentially-fitted Schemes

Abstract

In this paper an exponentially-fitted multiderivative method is developed for the numerical integration of the Schrödinger equation. We call the method multi-derivative since it uses derivatives of orders two and four. An application to the resonance problem of the radial Schrödinger equation indicates that the new method is more efficient than the Numerov method and other known methods found in the literature. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)