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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 12, Pages 803-812
http://dx.doi.org/10.1155/S0161171201003490

The residual and the error for collocation methods

1Computer Centre, University of Khartoum, Sudan
2Instituto de Matemática Pura e Aplicada, IMPA, Estrada Dona Castorina 110-Jardim Botânico, Rio de Janeiro CEP 22460-320, RJ, Brazil

Received 25 May 1999

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use earlier results on collocation matrices related to the solution and its derivatives in describing asymptotic relation between the error on the highest derivative and the residuals. That justifies the use of the form of the residual rather than its norm in measuring the error.