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The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

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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.