COMPUTER ALGEBRA PROGRAMS FOR THE CONSTRUCTION OF A FAMILY OF NUMEROV-TYPE EXPONENTIALLY-FITTED METHODS FOR THE NUMERICAL-SOLUTION OF THE SCHRODINGER-EQUATION

In this paper a computer algebra programme, written in the MAPLE (and REDUCE) language(s), is presented for the production of exponentially- fitted methods. By using this programme a family of predictor-correcto r exponential Numerov-type methods is obtained for the numerical solut ion of the coupled equations arising from the Schrodinger equation. Th e Numerov-type methods considered contain free parameters which allow them to be fitted to exponential functions. These new fourth algebraic order methods are very simple and integrate more exponential function s than both the well-known fourth order Numerov-type exponentially-fit ted methods and the sixth algebraic order Runge-Kutta type methods. Fr om the exponentially-fitted methods obtained using this computer algeb ra programme, a variable-step exponentially-fitted method is construct ed. Numerical results indicate that the new variable-step method is mu ch more efficient than other well-known methods for the numerical solu tion of the coupled equations arising from the Schrodinger equation. ( C) 1998 Elsevier Science Ltd. All rights reserved.