Quintic spline approach to the solution of a singularly-perturbed boundary-value problem

Authors:
T. Aziz;A. Khan
Affiliations:
Professor, Department of Applied Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India;Research Scholar, Department of Applied Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 1
Cited 1

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A collection of computational techniques for solving singular boundary-value problems

Advances in Engineering Software

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Abstract

A fourth-order uniform mesh difference scheme using quintic splines for solving a singularly-perturbed boundary-value problem of the form -εy"+p(x)y=f(x), p(x) 0, y(0) = α0, y(1) = α1, is derived. Our scheme leads to a pentadiagonal linear system. The convergence analysis is given and the method is shown to have fourth-order convergence. Numerical illustrations are given to confirm the theoretical analysis of our method.