IJPAM: Volume 75, No. 4 (2012)

BOUNDARY CHARACTERISTIC ORTHOGONAL
POLYNOMIALS FOR SINGULARLY PERTURBED PROBLEMS

Vivek Kumar
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
Year: 2012
Volume: 75
Issue: 4