Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions

Abstract

A new approach for constructing efficient Runge-Kutta-Nyström methods is introduced in this paper. Based on this new approach a new exponentially-fitted Runge-Kutta-Nyström fourth-algebraic-order method is obtained for the numerical solution of initial-value problems with oscillating solutions. The new method has an extended interval of periodicity. Numerical illustrations on well-known initial-value problems with oscillating solutions indicate that the new method is more efficient than other ones. © 2002 Elsevier Science Ltd. All rights reserved.