Malaysian Journal of Mathematical Sciences, May 2021, Vol. 15, No. 2
Improved Runge-Kutta Method with Trigonometrically-Fitting Technique for Solving Oscillatory Problem
Senu, N., Lee, K. C., Wan Ismail, W. F., Ahmadian, A., Ibrahim, S. N. I., and Laham, M. F.
Corresponding Email: norazak@upm.edu.my
Received date: 23 April 2020
Accepted date: 30 April 2021
Abstract:
In this article we propose a new method of Trigonometrically-Fitted Improved Runge-Kutta (TFIRK3(3)) with third-order and three stages for solving oscillatory ordinary differential equations. The proposed algorithm employs a derivation of method by adding trigonometric into
the Improved Runge-Kutta (IRK3(3)) method. It is found that the new method is more accurate as compared to IRK3(3) and classical Runge-Kutta methods. To illustrate the efficiency of this method, number of initial value problem for the system of first-order ordinary differential
equations (ODEs) are solved. The computational experiments show that the TFIRK3(3) method performs better than RK3(3), RK4(4), IRK3(3) and PHSFRK5(4) methods in most cases.
Keywords: Trigonometrically-fitted, ordinary differential equations, improved Runge-Kutta method, quantum cryptography, differential equations foundations, Schrödinger equations, computational experiments
Indexing
