@Article{IJNAM-11-2,
author = {paramasivam, M. and Miller, J., J., H. and Valarmathi, S.},
title = {Parameter-Uniform Convergence for a Finite Difference Method for a Singularly Perturbed Linear Reaction-Diffusion System with Discontinuous Source Terms},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2014},
volume = {11},
number = {2},
pages = {385--399},
abstract = {<p style="text-align: justify;">A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with discontinuous source terms is considered. A small positive parameter
multiplies the leading term of each equation. These singular perturbation parameters are assumed
to be distinct. The components of the solution exhibit overlapping boundary and interior layers.
A numerical method is constructed that uses a classical finite difference scheme on a piecewise
uniform Shishkin mesh. It is proved that the numerical approximations obtained by this method
are essentially first order convergent uniformly with respect to all of the perturbation parameters.
Numerical illustrations are presented in support of the theory.</p>},
issn = {2617-8710},
doi = {https://doi.org/2014-IJNAM-533},
url = {https://global-sci.com/article/83349/parameter-uniform-convergence-for-a-finite-difference-method-for-a-singularly-perturbed-linear-reaction-diffusion-system-with-discontinuous-source-terms}
}