@article{Ruby2025, 
author = { Ruby and Vembu Shanthi and Higinio Ramos},
title = {A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {6827-6852},
keywords = {convection diffusion, quasilinear, singular perturbation, Shishkin mesh, standard upwind scheme, backward Euler method, discontinuous source term, weak interior layer},
url = {https://www.sciopen.com/article/10.3934/math.2025313},
doi = {10.3934/math.2025313},
abstract = {The objective of the present paper is to solve a one-dimensional quasilinear parabolic singularly perturbed problem with a discontinuous source term. Due to the presence of such a discontinuity, an interior layer exists at the location of the discontinuity. The problem is solved by discretizing the spatial variable on a piecewise uniform Shishkin mesh using the standard upwind approach, while the backward Euler scheme is employed on a uniform mesh to discretize the time variable. The method is    ε-uniformly convergent, providing first-order convergence in the time domain and almost first-order convergence in the spatial variable. To validate the theoretical findings, the scheme was tested by numerically solving two examples.}
}