Robin boundary value problems for a singularly perturbed weakly coupled system of convection–diffusion equations having discontinuous source term

• Published in: The Journal of Analysis Vol. 28; no. 1; pp. 305 - 321
• Main Authors: Rao, S. Chandra Sekhara, Chawla, Sheetal
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.03.2020
• Subjects: Abstract Harmonic Analysis; Analysis; Fourier Analysis; Functional Analysis; Mathematics; Mathematics and Statistics; Measure and Integration; Proceedings: ICMAA 2016; Special Functions; Finite difference scheme; 65M15; Shishkin mesh; Uniformly convergent; 65M06; Singular perturbation problems; Weakly coupled system; Overlapping boundary layers; Interior layers; Discontinuous source term; Convection–diffusion; 65M12
• ISSN: 0971-3611; 2367-2501
• DOI: 10.1007/s41478-019-00172-6

In this paper, we consider a weakly coupled system of convection–diffusion equations subject to Robin boundary conditions, and having boundary and interior layers. The diffusion term of each equation is multiplied by a small singular perturbation parameter, but these parameters are assumed to be different in magnitude, and the source term is having a discontinuity at a point in the interior of the domain. An upwind scheme is used for the considered problem in conjunction with piecewise uniform Shishkin mesh. It is proved that the numerical approximations produced by this method are almost first order uniformly convergent with respect to both small parameters. Numerical results are presented to validate the theoretical results.