@article{Chandru2024, 
author = {M. Chandru and T. Prabha and V. Shanthi and H. Ramos},
title = {An almost second order uniformly convergent method for a two-parameter singularly perturbed problem with a discontinuous convection coefficient and source term},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24998-25027},
keywords = {two-parameter singularly perturbed problem, boundary and interior layers, hybrid numerical scheme, parameter-uniform convergence},
url = {https://www.sciopen.com/article/10.3934/math.20241219},
doi = {10.3934/math.20241219},
abstract = {In this paper, we discuss a higher-order convergent numerical method for a two-parameter singularly perturbed differential equation with a discontinuous convection coefficient and a discontinuous source term. The presence of perturbation parameters generates boundary layers, and the discontinuous terms produce interior layers on both sides of the discontinuity. In order to obtain a higher-order convergent solution, a hybrid monotone finite difference scheme is constructed on a piecewise uniform Shishkin mesh, which is adapted inside the boundary and interior layers. On this mesh (including the point of discontinuity), the present method is almost second-order parameter-uniform convergent. The current scheme is compared with the standard upwind scheme, which is used at the point of discontinuity. The numerical experiments based on the proposed scheme show higher-order (almost second-order) accuracy compared to the standard upwind scheme, which provides almost first-order parameter-uniform convergence.}
}