The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term

Rao, S. Chandra Sekhara; Chawla, Sheetal

doi:10.1007/978-3-030-11539-5_18

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suitable conditions on the appropriate mesh generating functions are derived, which are sufficient for the parameter-uniform convergence of the method in the discrete maximum norm with an optimal error bound on the Bakhalov-Shishkin mesh and Shishkin mesh. Singularly perturbed system of steady and unsteady reaction-diffusion problems with continuous/discontinuous source terms are considered in [21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis for a class of coupled system of singularly perturbed time‐dependent convection‐diffusion equations with a discontinuous source term

Rao

Chawla

Chaturvedi

2021

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

In this article, we present a parameters‐uniform numerical method for a time‐dependent weakly coupled system of two convection‐diffusion equations that has a discontinuity, along the line x=d, in the source term. The second order term of each equation is multiplied by a small singular perturbation parameter and these parameters are assumed to be different in magnitude. On an appropriate Shishkin mesh, the considered problem is discretized using an upwind central difference scheme away from the line of discontinuity, and a particular upwind central difference scheme along the line of discontinuity. The numerical approximations produced by this scheme are uniformly convergent of first‐order in time and almost first‐order in space with respect to both perturbation parameters. Numerical results are presented to validate the theoretical results.

show abstract