Year: 1984
Journal of Computational Mathematics, Vol. 2 (1984), Iss. 1 : pp. 56–69
Abstract
The correction procedure has been discussed by L. Fox and V. Pereyra for accelerating the convergence of a certain approximate solution. Its theoretical basis is the existence of an asymptotic expansion for the error of discretization proved by Filippov and Rybinskii and Stetter: u−uh=h2v+O(h4), where u is the solution of the original differential equation, uh the solution of the approximate finite difference equation with parameter h and v the solution of a correction differential equation independent of h. Stetter et al. used the extrapolation procedure to eliminate the auxiliary function v while Pereyra et al. used some special procedure to solve v approximately.
In the present paper we will present a difference procedure for solving v easily.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1984-JCM-9640
Journal of Computational Mathematics, Vol. 2 (1984), Iss. 1 : pp. 56–69
Published online: 1984-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14