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Mesh Selection in Collocation for Boundary Value Problems

Lookup NU author(s): Dr Kenneth Wright

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Abstract

This paper introduces some subdivision criterion functions for use in adaptive algorithms for the solution of linear ordinary differential equations by piecewise polynomial collocation methods. These criterion functions aim to take into account the influence of the behaviour in one subinterval on the error in others. They are compared with various alternatives using examples which include problems with interior or boundary layers. These examples illustrate some of the difficulties which can arise. The danger of using criterion functions based on estimates of the global error is emphasized.

Publication metadata

Author(s): Wright K, Ahmed AHA, Seleman AH

Publication type: Article

Publication status: Published

Journal: IMA Journal of Numerical Analysis

Year: 1991

Volume: 11

Issue: 1

Pages: 7-20

ISSN (print): 0272-4979

ISSN (electronic): 1464-3642

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1093/imanum/11.1.7

DOI: 10.1093/imanum/11.1.7

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