Optimizing a class of linear multi-step methods for the approximate solution of the radial Schrödinger equation and related problems with respect to phase-lag

Theodore Simos
  • 1 Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia
  • 2 Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100, Tripolis, Greece
  • 3 International Institute for Theoretical Physics and Mathematics Einstein-Galilei, Via Santa Gonda, 14 -59100, PRATO, Italy

Abstract

In this paper we consider a methodology of optimization of the efficiency of a numerical method for the approximate solution of the radial Schrödinger equation and related problems. More specifically, we show how the methodology of vanishing of the phase-lag and its derivatives optimizes the behaviour of a numerical method.

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