Solving Oscillatory Problems Using Trigonometrically-Fitting Improved Runge-Kutta Nystrom Method

Abstract

   In this article, we suggest a new technique for solving oscillatory ordinary differential equations called Trigonometrically Fitted Improved Runge-Kutta Nystrom (TFIRKN4) method, which has three stages and fourth order. The Improved Runge-Kutta Nystrom (IRKN4) method is extended with trigonometric calculations in the proposed approach. The coefficients of the proposed method are based on the frequency and step size. It is discovered that the new method is more precise when compared to the existing Runge-Kutta Nystrom and IRKN4 methods. The number of test problems for the second-order ordinary differential equations (ODEs) is solved to demonstrate the effectiveness of this approach. According to the computational experiments, the TFIRKN4 approach consistently outperforms the IRKN4 and existing Runge-Kutta Nystrom methods.