Tenth Order Compact Finite Difference Method for Solving Singularly Perturbed 1D Reaction

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International Journal of Engineering and Applied Sciences
Volume:8 Issue:3
Tenth Order Compact Finite Difference Method for Solving Singularly Perturbed 1D Reaction - Diffusio...

Tenth Order Compact Finite Difference Method for Solving Singularly Perturbed 1D Reaction - Diffusion Equations

Authors : Fasika Wondimu Galu, Gemechis File DURESSA, Tesfaye Aga BULLO

Pages : 15-24

Doi:10.24107/ijeas.255031

View : 87 | Download : 7

Publication Date : 2016-10-10

Article Type : Research Paper

Abstract :In this paper, tenth order compact finite difference method have been presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. The derivatives in the given differential equation have been replaced by finite difference approximations and transformed to tri-diagonal system which can easily be solved by Discrete Invariant Imbedding algorithm. The theoretical error bounds have been established for the method. Three model examples have been considered to check the applicability of the proposed method. The numerical results presented in tables show that the present method approximates the exact solution very well.
Keywords : Singular perturbation, compact differential difference method, reaction diffusion equations

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