Optimized fourth-order Runge-Kutta method for solving oscillatory problems

• Main Authors: Hussain, Kasim Abbas, Ismail, Fudziah, Senu, Norazak, Rabiei, Faranak
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/57172/1/Optimized%20fourth-order%20Runge-Kutta%20method%20for%20solving%20oscillatory%20problems.pdf; http://psasir.upm.edu.my/id/eprint/57172/; http://aip.scitation.org/doi/abs/10.1063/1.4952512
• Institution: Universiti Putra Malaysia

In this article, we develop a Runge-Kutta method with invalidation of phase lag, phase lag's derivatives and amplification error to solve second-order initial value problem (IVP) with oscillating solutions. The new method depends on the explicit Runge-Kutta method of algebraic order four. Numerical tests from its implementation to well-known oscillatory problems illustrate the robustness and competence of the new method as compared to the well-known Runge-Kutta methods in the scientific literature.