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

Year 2016, Volume: 8 Issue: 3, 15 - 24, 10.10.2016

Fasika Wondimu Galu Gemechis File Duressa , Tesfaye Aga Bullo

https://doi.org/10.24107/ijeas.255031

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equation have been replaced by finite difference approximations and transformed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

References

• Farrell, A. F., Miller, J. J. H., O’Riordan, E and Shishkin, G. I., Robust Computational Techniques for Boundary Layers. Chapman-Hall/CRC, New York, 2000.