A NUMERICAL PERTURBATION EXPANSIONMETHOD FOR THE SOLUTION OF ALIENARD-TYPE INITIAL-VALUE PROBLEMWITH PERIODIC DECAYING FORCING TERM

摘要

A numerical perturbation expansion method is developed, analysed and implemented for the numerical solution of a second-order initial-value problem. The differential equation in this problem exhibits cubic damping, a cubic restoring force and a decaying forcing-term which is periodic with constant frequency. The method is compared with the numerical method by Twizell [1]. In fact, the later is first perturbation approximate solution in the present paper.