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Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes

Calvo, M.C. and Higham, D.J. and Montijano, J.M. and Rández, L. (1997) Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes. Advances in Computational Mathematics, 7 (3). pp. 361-382. ISSN 1019-7168

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Abstract

The potential for adaptive explicit Runge-Kutta (ERK) codes to produce global errors that decrease linearly as a function of the error tolerance is studied. It is shown that this desirable property may not hold, in general, if the leading term of the locally computed error estimate passes through zero. However, it is also shown that certain methods are insensitive to a vanishing leading term. Moreover, a new stepchanging policy is introduced that, at negligible extra cost, ensures a robust global error behaviour. The results are supported by theoretical and numerical analysis on widely used formulas and test problems. Overall, the modified stepchanging strategy allows a strong guarantee to be attached to the complete numerical process.

Item type: Article
ID code: 189
Keywords: initial value problems, Runge-Kutta methods, stepsize control, mathematics, computer science, Electronic computers. Computer science, Mathematics, Computational Mathematics, Applied Mathematics
Subjects: Science > Mathematics > Electronic computers. Computer science
Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Ms Sarah Scott
    Date Deposited: 01 Mar 2006
    Last modified: 04 Sep 2014 10:00
    URI: http://strathprints.strath.ac.uk/id/eprint/189

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