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International Journal of Mathematical Research

February 2013, Volume 2, 1, pp 1-10

Spline Methods for a Class of Singularly Perturbed Boundary Value Problems

O.M. Ogunlaran

,

O.A. Taiwo

O.M. Ogunlaran 1
O.A. Taiwo 2

  1. Department of Mathematics and Statistics, Bowen University, Iwo, Nigeria 1

  2. Department of Mathematics, University of Ilorin, Ilorin, Nigeria 2

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Abstract:

In this paper, we develop numerical methods based on a non-polynomial spline function with uniform grid for solving certain class of singularly perturbed boundary value problems. The proposed methods are second-order and fourth-order accurate. Numerical examples are provided to demonstrate the efficiency of the proposed methods.

Contribution/ Originality

Keywords:

Non-polynomial Spline; Singular perturbation; Boundary value problems

Reference:

  1. S. Natesan and B. S. Deb, "A robust computational method for singularly perturbed coupled system of reaction-diffusion boundary value problem," Appl. Math. Comput., vol. 188, pp. 353-364, 2007.
  2. L. Abrahamson and S. Osher, "Monotone difference schemes for singular perturbation problems," SIAM J. Numer. Anal., vol. 19, pp. 979-992, 1982.
  3. K. Surla and M. Stojanovic, "Solving singularly perturbed boundary value problems by splines in tension," J. Comput.  Appl. Math., vol. 24, pp. 355-363, 1988.
  4. M. K. Kadalbajoo and R. K. Bawa, "Variable-mesh difference scheme for singularly perturbed boundary value problem using splines," J. Optimization Theory and Appl., pp. 405-416, 1996.

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