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Numerical Solution of Singular Perturbation problems via deviating Argument through the Numerical methods

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Author Affiliations

  • 1Kakatiya Institute of Technolog and Science, warangal- 506015, INDIA
  • 2Kakatiya Institute of Technolog and Science, warangal- 506015, INDIA
  • 3Kakatiya Institute of Technolog and Science, warangal- 506015, INDIA

Res. J. Mathematical & Statistical Sci., Volume 2, Issue (9), Pages 9-19, September,12 (2014)

Abstract

An attempt is made in this article to obtain the numerical solution of singularly perturbed two point boundary value problems. To achieve this singular perturbation problem is reduced to first order differential equation by taking a small deviating argument. The Simpsons 3/8 rule is employed to get the equation in y (xi). Hermite interpolation is used to obtain the value of y at the intermediate points of the boundary, finally yielding to a tridiagonal system of equations. The discrete invariant imbedding method is used to obtain the solution of system of equations. four linear singular perturbation problems of which two are with constant coefficients and two are with variable coefficients are solved to test the applicability and competence of the proposed method. The numerical results obtained by the proposed method are compared with the exact solution and also with the results obtained using Simpsons 1/3 rule. It is observed that the numerical results are very near to the exact solution.

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