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Adaptive methods for piecewise polynomial collocation for ordinary differential equations

Lookup NU author(s): Dr Kenneth Wright

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Abstract

Various adaptive algorithms for the solution of ordinary differential boundary value problems using piecewise polynomial collocation are considered. Five different criteria are compared using both interval subdivision and mesh redistribution. All the algorithms are based on the idea of equidistribution of a criterion. It is, however, shown that when accuracy is poor that equidistribution may not give a unique solution. The main results indicate that mesh redistribution is more reliable than interval subdivision, and give an evaluation of the five criteria.

Publication metadata

Author(s): Wright K

Publication type: Article

Publication status: Published

Journal: BIT Numerical Mathematics

Year: 2007

Volume: 47

Issue: 1

Pages: 197-212

Date deposited: 26/11/2004

ISSN (print): 0006-3835

ISSN (electronic): 1572-9125

Publisher: Springer Netherlands

URL: http://dx.doi.org/10.1007/s10543-006-0103-y

DOI: 10.1007/s10543-006-0103-y

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