TY  - JOUR
AU  - Chandru, M.
AU  - Prabha, T.
AU  - Shanthi, V.
AU  - Ramos, H.
PY  - 2024
TI  - An almost second order uniformly convergent method for a two-parameter singularly perturbed problem with a discontinuous convection coefficient and source term
JO  - AIMS Mathematics
SP  - 24998
EP  - 25027
VL  - 9
IS  - 9
AB  - 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.
UR  - https://doi.org/10.3934/math.20241219
DO  - 10.3934/math.20241219