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International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 89-96
http://dx.doi.org/10.1155/S0161171295000123

Computable error bounds for collocation methods

Department of Mathematics, Ash-Sharq University, Khartoum, Sudan

Received 12 August 1992; Revised 27 February 1994

Copyright © 1995 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

This paper deals with error bounds for numerical solutions of linear ordinary differential equations by global or piecewise polynomial collocation methods which are based on consideration of the involved differential operator, related matrices and the residual. It is shown that significant improvement may be obtained if direct bounds for the error in the solution are considered. The practical implementation of the theory is illustrated by a selection of numerical examples.