A fourth-order four-stage trigonometrically-fitted improved Runge-Kutta method for oscillatory initial value problems

Abstract

The present work pertains to the derivation, analysis and application of a fourth-order four-stage trigonometrically-fitted Improved Runge-Kutta (TFIRK4-4) method for solving the initial value problem (IVP) y^' (x)=f(x,y(x)). The method is known to integrate exactly the initial value problem whose solution is a linear combination of the functions sin⁡(ωx) and cos⁡(ωx), or equivalently e^iωx and e^(-iωx), where ω>0, being the principal frequency of the problem, is used to enhanced the accuracy of the method. The numerical results show the efficacy of the new method in comparison with other existing methods.