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Global error versus tolerance for explicit Runge-Kutta methods

Higham, Desmond J. (1991) Global error versus tolerance for explicit Runge-Kutta methods. IMA Journal of Numerical Analysis, 11 (4). pp. 457-480. ISSN 0272-4979

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Abstract

Initial value solvers typically input a problem specification and an error tolerance, and output an approximate solution. Faced with this situation many users assume, or hope for, a linear relationship between the global error and the tolerance. In this paper we examine the potential for such 'tolerance proportionality' in existing explicit Runge-Kutta algorithms. We take account of recent developments in the derivation of high-order formulae, defect control strategies, and interpolants for continuous solution and first derivative approximations. Numerical examples are used to verify the theoretical predictions. The analysis draws on the work of Stetter, and the numerical testing makes use of the nonstiff DETEST package of Enright and Pryce.

Item type: Article
ID code: 206
Keywords: Runge-Kutta Methods, numerical mathematics, high-order formulae, DETEST package, Mathematics, Computational Mathematics, Applied Mathematics, Mathematics(all)
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Ms Sarah Scott
    Date Deposited: 09 Mar 2006
    Last modified: 04 Sep 2014 09:53
    URI: http://strathprints.strath.ac.uk/id/eprint/206

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