IJPAM: Volume 75, No. 4 (2012)
POLYNOMIALS FOR SINGULARLY PERTURBED PROBLEMS
Department of Applied Mathematics
Delhi Technological University
Bawana Road, Delhi, 110042, INDIA
Abstract. In this paper we generate fitted mesh using the boundary characteristic orthogonal polynomials for numerically solving singularly perturbed boundary value problems. The method is based upon the orthogonal collocation method. Boundary characteristic orthogonal polynomials (BCOPs) are generated using the Gram - Schmit process from a set of linearly independent functions which also satisfy the given boundary conditions. The procedure is illustrated by taking several examples. After obtaining the fitted mesh, the problems have been solved using upwind finite difference method.
Received: August 6, 2011
AMS Subject Classification: 65L11, 65L10, 65L50, 65M50
Key Words and Phrases: boundary characteristic orthogonal polynomials (BCOPs), singularly perturbed boundary values problems (SPPs), fitted mesh methods, upwind finite difference
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395