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

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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

$$ - \varepsilon y'' + p(x)y = f(x),{\text{ }}p(x) >0,$$
$$y(0) = \alpha _0 ,{\text{ }}y(1) = \alpha _1 ,$$

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    T. Aziz (Professor)

  2. Department of Applied Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    A. Khan (Research Scholar)

Authors
  1. T. Aziz
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  2. A. Khan
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Aziz, T., Khan, A. Quintic Spline Approach to the Solution of a Singularly-Perturbed Boundary-Value Problem. Journal of Optimization Theory and Applications 112, 517–527 (2002). https://doi.org/10.1023/A:1017959915002

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