Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers

Sheetal Chawla (), Urmil () and Jagbir Singh ()
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Sheetal Chawla: Pt. N.R.S. Government College Rohtak
Urmil: Maharshi Dayanand University
Jagbir Singh: Maharshi Dayanand University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 675-688

Abstract: Abstract In the present paper, Robin boundary value problem for a system of singularly perturbed reaction-diffusion equations with discontinuous source term is studied. The highest order derivative in each equation is multiplied by the perturbation parameters which are different in magnitude. The considered system does not obey maximum principle. Forward-backward approximation is used for the Robin boundary conditions and a central finite difference approximation is proposed for the differential system in conjunction with piecewise uniform Shishkin meshes and graded Bakhvalov meshes. The scheme is proved to be an almost first-order parameter uniform convergent. Numerical experiments are presented which are in line with the theoretical findings.

Keywords: Singular perturbation; Parameter-uniform convergence; Discontinuous source term; Boundary layers; Internal layers; Shishkin meshes; Bakhvalov meshes; Reaction-diffusion equation; 65M06; 65M12; 65M15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00285-y

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