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.
CITATION STYLE
Hamid, F. N. A., Rabiei, F., & Ismail, F. (2016). Composite group of explicit Runge-Kutta methods. In AIP Conference Proceedings (Vol. 1739). American Institute of Physics Inc. https://doi.org/10.1063/1.4952537
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