Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations

Che Jawias, Nur Izzati and Ismail, Fudziah and Suleiman, Mohamed and Jaafar, Azmi (2010) Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations. Malaysian Journal of Mathematical Sciences, 4 (1). pp. 95-105. ISSN 1823-8343

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Abstract

A new fourth order four-stage diagonally Implicit Runge-Kutta (DIRK) method which is specially designed for the integration of Linear Ordinary Differential Equations (LODEs) is constructed. In the derivation, Butcher's error equations are used but one of the error equations can be eliminated due to the property of the LODE itself. The stability aspect of the method is investigated and it is found to have a bigger region of stability compared to explicit Runge-Kutta (ERK) method of the same type (designed for the integration of LODE). A set of test problems are used to validate the method and numerical results show that the method produced smaller global error compared to ERK method.

Item Type:Article
Keyword:Linear ODEs; Fourth order
Subject:Differential equations - Numerical solutions
Subject:Runge-Kutta formulas
Faculty or Institute:Faculty of Computer Science and Information Technology
Publisher:UPM Press
ID Code:14811
Deposited By: Umikalthom Abdullah
Deposited On:14 May 2012 06:26
Last Modified:17 Dec 2012 01:41

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