AUTHOR=Kehinde Olawale O. , Munyakazi Justin B. , Appadu Appanah R. 

TITLE=A NSFD Discretization of Two-Dimensional Singularly Perturbed Semilinear Convection-Diffusion Problems

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=8

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.861276

DOI=10.3389/fams.2022.861276

ISSN=2297-4687

ABSTRACT=<p>Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent. In this article, we study a two-dimensional semilinear singularly perturbed convection-diffusion problems. Our approach requires linearization of the continuous semilinear problem using the quasilinearization technique. We then discretize the resulting linear problems in the framework of non-standard finite difference methods. A rigorous convergence analysis is conducted showing that the proposed method is first-order parameter-uniform convergent. Finally, two test examples are used to validate the theoretical findings.</p>