A fifth-order five-stage trigonometrically-fitted improved Runge-Kutta method for oscillatory initial value problems

Abstract

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 analysed in this work. The method is shown to integrate exactly the initial value problem whose solution is a linear combination of the set functions sin⁡(ωx) and cos⁡(ωx) for trigonometrically fitted, and e^iωx and e^(-iωx) for exponentially fitted, where ω>0∈R, 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.