A Fifth-Order Five-Stage Trigonometrically-Fitted Improved Runge-Kutta Method for Oscillatory Initial Value Problems

Abstract

Aliyu Umar Mustapha, Abdulrahman Ndanusa, and Ismail Gidado Ibrahim

A fifth-order five-stage trigonometrically-fitted Improved Runge-Kutta (TFIRK5-5) method for solving first-order initial value problems (IVPs) has been derived and analyzed in this work. The method is shown to integrate exactly the initial value problem whose solution is a linear combination of the set functions and trigonometrically fitted. For exponentially fitted, where, being the main frequency of the problem, is used to increase the accuracy of the method. The numerical results revealed the effectiveness of the new method in comparison with other existing methods in the literature.