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http://dx.doi.org/10.12941/jksiam.2013.17.221

AN INITIAL VALUE METHOD FOR SINGULARLY PERTURBED SYSTEM OF REACTION-DIFFUSION TYPE DELAY DIFFERENTIAL EQUATIONS  

Subburayan, V. (Department of Mathematics, SRM University)
Ramanujam, N. (Department of Mathematics, Bharathidasan University)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.17, no.4, 2013 , pp. 221-237 More about this Journal
Abstract
In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.
Keywords
Weakly coupled system; Reaction-diffusion type equations; Initial value method; Shishkin mesh; Delay; Negative shift;
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