Improved Runge-Kutta Method for Oscillatory Problem Solution Using Trigonometric Fitting Approach

This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an character in the solutions. Compared traditional method, (IRK) is natural two-step requiring fewer steps. The suggested extends fourth-order (IRK4) with trigonometric calculations. approach intended integrate problems particular initial value (IVPs) using set functions and for trigonometrically fitted. To improve method's accuracy, problem primary frequency used. novel more accurate than conventional IRK4. Several test system first-order ordinary differential equations carry out numerically demonstrate effectiveness this approach. computational studies show that TFIRK4 efficient existing methods.