Quintic Spline Approach to the Solution of a Singularly-Perturbed Boundary-Value Problem

Tariq Aziz () and A. Khan
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A. Khan: Aligarh Muslim University

Journal of Optimization Theory and Applications, 2002, vol. 112, issue 3, No 3, 517-527

Abstract: Abstract A fourth-order uniform mesh difference scheme using quintic splines for solving a singularly-perturbed boundary-value problem of the form $$ - \varepsilon y'' + p(x)y = f(x),{\text{ }}p(x) >0,$$ $$y(0) = \alpha _0 ,{\text{ }}y(1) = \alpha _1 ,$$ 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.

Keywords: Singularly-perturbed boundary-value problems; quintic splines; monotone matrices; boundary layers; uniform convergence (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1017959915002

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