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http://dx.doi.org/10.14317/jami.2016.495

A SCHWARZ METHOD FOR FOURTH-ORDER SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEM WITH DISCONTINUOUS SOURCE TERM  

CHANDR, M. (Department of Mathematics, National Institute of Technology)
SHANTHI, V. (Department of Mathematics, National Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.34, no.5_6, 2016 , pp. 495-508 More about this Journal
Abstract
A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.
Keywords
Singularly Perturbed Problems; Ordinary Differential Equations; Reaction-Diffusion; Interior layer; Higher Order;
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