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

In this paper, the Trigonometrically Fitted Improved Runge-KuttaNystrom method is proposed as a novel method with four stages and fifth order for solving oscillatory problems. This method is intended to integrate second-order initial value problems using the trigonometrically fitting approach. To increase the method'saccuracy, the principal frequency of the problem푤∈ℝ, is used. It is discovered that the new method is more precise when compared with the other existing Runge-Kutta Nystrom and IRKN5 methods. To show how well the TFIRKN5 method works, test problems for second-order ordinary differential equations (ODEs) are solved. The numerical outcomes show that the novel approach outperforms methods that have already been published.