Composite group of explicit Runge-Kutta methods

• Main Authors: Abd Hamid, Fatin Nadiah, Rabiei, Faranak, Ismail, Fudziah
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/57159/1/Composite%20group%20of%20explicit%20Runge-Kutta%20methods.pdf; http://psasir.upm.edu.my/id/eprint/57159/; http://aip.scitation.org/doi/abs/10.1063/1.4952537
• Institution: Universiti Putra Malaysia

In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method.