An almost second order fem for a weakly coupled system of two singularly perturbed differential equations of reaction-diffusion type with discontinuous source term

Authors:
A. Ramesh Babu;N. Ramanujam
Affiliations:
Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India;Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India
Venue:
Neural, Parallel & Scientific Computations - Special issue on computational techniques for differential equations will applications
Year:
2009

Citing 4
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Differentiability properties of solutions of the equation -ε2δ u + ru=f(x,y) in a square

SIAM Journal on Mathematical Analysis
Singular perturbation methods for ordinary differential equations

Singular perturbation methods for ordinary differential equations
Sufficient conditions for uniform convergence on layer-adapted grids

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A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term

Journal of Computational and Applied Mathematics

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Abstract

In this paper, we consider a Boundary Value Problem(BVP) for a weakly coupled system of two singularly perturbed ordinary differential equations of reaction-diffusion type with discontinuous source term. The solution of this type of problem exhibits boundary and interior layers. A numerical method based on finite element method on Shishkin and Bakhvalov-Shishkin meshes is presented. We derive an error estimate of order O(N-2 ln2 N) in the maximum norm. Numerical experiments are also presented to support our theoretical results.