A NSFD Discretization of Two-Dimensional Singularly Perturbed Semilinear Convection-Diffusion Problems - Kehinde, Olawale O.; Munyakazi, Justin B.; Appadu, Appanah R. (Frontiers in Applied Mathematics and Statistics, 2022)
Despite the availability of an abundant literature on singularly perturbed problems, interest toward nonlinear problems is very limited to date. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-nonexistent. In this paper, 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 nonstandard 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.