Non-standard difference schemes for singular perturbation problems revisited

Non-standard finite difference techniques for solving various linear two-point singularly perturbed boundary value problems are considered. They consist of replacing the original differential equation by a related differential equation with a small deviating argument. This related problem is then di...

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Bibliographic Details
Published in:Applied mathematics and computation 1998-06, Vol.92 (2), p.101-123
Main Authors: Varner, T.N., Choudhury, S.Roy
Format: Article
Language:English
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Summary:Non-standard finite difference techniques for solving various linear two-point singularly perturbed boundary value problems are considered. They consist of replacing the original differential equation by a related differential equation with a small deviating argument. This related problem is then discretized using finite differences. This discretized problem is solved using standard matrix methods. The accuracy and robustness of these numerical schemes are then carefully investigated, and compared to standard centered finite differences. In particular, earlier claims for the superiority of such schemes over standard finite differences are shown to be invalid.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(97)10025-X