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Robust defect control with Runge-Kutta schemes

Higham, D.J. (1989) Robust defect control with Runge-Kutta schemes. SIAM Journal on Numerical Analysis, 26 (5). pp. 1175-1183. ISSN 0036-1429

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Abstract

Enright [Numerical Analysis Report 122, University of Manchester, Manchester, U.K., 1986] implements a Runge-Kutta method for solving the initial value problem using an alternative to the standard local error control scheme. The aim is to control the defect associated with a local interpolant by sampling its value at one or more fixed points within each step. However, in general, the quality of a sample point is problem-dependent and also varies from step to step. Two classes of interpolant are presented for which the asymptotic behaviour of the defect is known a priori, allowing optimal sample points to be chosen.

Item type: Article
ID code: 211
Keywords: Runge-Kutta formula, defect, interpolation, numerical mathematics, Mathematics, Numerical Analysis
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
Depositing user: Ms Sarah Scott
Date Deposited: 08 Mar 2006
Last modified: 04 Sep 2014 09:52
URI: http://strathprints.strath.ac.uk/id/eprint/211

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