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International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 375-379
http://dx.doi.org/10.1155/S0161171298000519

Computable error bounds with improved applicability conditions for collocation methods

Instituto de Matematica Pura e Aplicada, IMPA, Estrada Dona Castorina 110 - Jardim Botanico, Rio de Janeiro CEP 22460-320, RJ, Brazil

Received 10 July 1995; Revised 5 February 1997

Copyright © 1998 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 is concerned with error bounds for numerical solution of linear ordinary differential equation using collocation method. It is shown that if the differential operator is split in different operator forms then the applicability conditions for the computable error bounds which are based on the collocation matrices could be improved