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Analysis of the dynamics of local error control via a piecewise continuous residual

Higham, D.J. and Stuart, A.M. (1998) Analysis of the dynamics of local error control via a piecewise continuous residual. BIT Numerical Mathematics, 38 (1). pp. 44-57. ISSN 0006-3835

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Abstract

Positive results are obtained about the effect of local error control in numerical simulations of ordinary differential equations. The results are cast in terms of the local error tolerance. Under the assumption that a local error control strategy is successful, it is shown that a continuous interpolant through the numerical solution exists that satisfies the differential equation to within a small, piecewise continuous, residual. The assumption is known to hold for the MATLAB ode23 algorithm [10] when applied to a variety of problems.Using the smallness of the residual, it follows that at any finite time the continuous interpolant converges to the true solution as the error tolerance tends to zero. By studying the perturbed differential equation it is also possible to prove discrete analogs of the long-time dynamical properties of the equation-dissipative, contractive and gradient systems are analysed in this way.

Item type: Article
ID code: 185
Keywords: error control, continuous interpolants, dissipativity, contractivity, gradient systems, computer science, software engineering, mathematics, Electronic computers. Computer science, 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: 02 Mar 2006
Last modified: 12 Mar 2012 10:35
URI: http://strathprints.strath.ac.uk/id/eprint/185

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