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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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Official URL: http://einspem.upm.edu.my/journal/volume4.1.php

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
Faculty or Institute:Faculty of Computer Science and Information Technology
Faculty of Science
Publisher:Universiti Putra Malaysia Press
ID Code:14811
Deposited By: Umikalthom Abdullah
Deposited On:14 May 2012 14:26
Last Modified:27 May 2015 14:37

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