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An improved theta-method for systems of ordinary differential equations

Lubuma, J.M.-S. and Roux, R. (2003) An improved theta-method for systems of ordinary differential equations. Journal of Difference Equations and Applications, 9 (11). pp. 1023-1035. ISSN 1563-5120

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Abstract

The θ-method of order 1 or 2 (if θ=1/2) is often used for the numerical solution of systems of ordinary differential equations. In the particular case of linear constant coefficient stiff systems the constraint 1/2 ≤ θ ≤1, which excludes the explicit forward Euler method, is essential for the method to be A -stable. Moreover, unless θ=1/2, this method is not elementary stable in the sense that its fixed-points do not display the linear stability properties of the fixed-points of the involved differential equation. We design a non-standard version of the θ-method of the same order. We prove a result on the elementary stability of the new method, irrespective of the value of the parameter θ ∈[0,1]. Some absolute elementary stability properties pertinent to stiffness are discussed.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 05 Feb 2009 18:27
Last Modified: 05 Feb 2009 18:27
Published Version: http://dx.doi.org/10.1080/1023619031000146904
Status: Published
Publisher: Taylor & Francis
Identification Number: 10.1080/1023619031000146904
URI: http://eprints.whiterose.ac.uk/id/eprint/6604

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