Numerical Solution of Singularly Perturbed Delay Reaction-Diffusion Equations with Layer or Oscillatory Behaviour

Gemechis File¹, Gashu Gadisa¹, Tesfaye Aga¹ and Y. N. Reddy^2,

¹Department of Mathematics, Jimma University, Jimma, P. O. Box 378, Ethiopia

²Department of Mathematics, National Institute of Technology, Warangal-506 004, India

Cite this paper:
Gemechis File, Gashu Gadisa, Tesfaye Aga and Y. N. Reddy. Numerical Solution of Singularly Perturbed Delay Reaction-Diffusion Equations with Layer or Oscillatory Behaviour. American Journal of Numerical Analysis. 2017; 5(1):1-10. doi: 10.12691/ajna-5-1-1

Abstract

In this paper, we presented numerical method for solving singularly perturbed delay differential equations with layer or oscillatory behaviour for which a small shift (δ) is in the reaction term. First, the given singularly perturbed delay reaction-diffusion equation is converted into an asymptotically equivalent singularly perturbed two point boundary value problem and then solved by using fourth order finite difference method. The stability and convergence of the method has been investigated. The numerical results have been tabulated and further to examine the effect of delay on the boundary layer and oscillatory behavior of the solution, graphs have been given for different values of δ. Both theoretical and numerical rate of convergence have been established and are observed to be in agreement for the present method. Briefly, the present method improves the findings of some existing numerical methods in the literature.

Keywords:
singularly perturbed problem delay reaction-diffusion equation oscillatory behaviour

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