A family of four-step exponential fitted methods for the numerical integration of the radial Schrödinger equation

Abstract

A family of exponential four-step methods is developed for the numerical integration of the one-dimensional Schrödinger equation. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. The new methods integrate more exponential functions, and are very simple compared with the well-known sixth algebraic order Runge-Kutta type methods. Numerical results indicate that the new methods are much more accurate than other exponentially fitted methods.