Composite group of explicit Runge-Kutta methods

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 funct...

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Bibliographic Details
Main Authors: Hamid, Fatin Nadiah Abd, Rabiei, Faranak, Ismail, Fudziah
Format: Conference Proceeding
Language:English
Subjects:
Boundary value problems
Differential equations
Methods
Ordinary differential equations
Runge-Kutta method
Online Access:Get full text
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Summary: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.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4952537