A Third Order Trigonometrically-Fitted Improved Runge-Kutta Method for Oscillatory Problems

Abstract

This research is concerned about improving the numerical solution of initial value problems with oscillatory solutions by trigonometrically – fitting a third order Improved Runge – Kutta (IRK) method with coefficients that are dependent on the frequency and step – size. Numerical experiments with sample problems compared the results of the proposed trigonometrically – fitted method with those of the non – fitted method. It was established that the trigonometrically-fitted third order three stage IRK method, IRK32, is more efficient in terms of fewer number of function evaluations and accurate in terms of small errors than non-fitted IRK method of same order.