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Composite group of explicit Runge-Kutta methods

Abd Hamid, Fatin Nadiah and Rabiei, Faranak and Ismail, Fudziah (2016) Composite group of explicit Runge-Kutta methods. In: 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016), 26-28 Jan. 2016, Kuala Lumpur, Malaysia. pp. 1-7.

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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.

Item Type:Conference or Workshop Item (Paper)
Keyword:Composite groups; Runge-Kutta methods
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:AIP Publishing
DOI Number:10.1063/1.4952537
ID Code:57159
Deposited By: Nabilah Mustapa
Deposited On:08 Sep 2017 13:20
Last Modified:08 Sep 2017 13:20

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