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

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 The derivatives in the given differential equation have been replaced by finite difference approximations and transformed to tri-diagonal system which can easily be solved by Discrete Invariant Imbedding algorithm.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

1. 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.