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

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 semilinear are quasi-non-existent. this article, we study a two-dimensional convection-diffusion problems. Our approach requires linearization continuous problem using quasilinearization technique. We then discretize resulting linear in framework non-standard finite difference methods. A rigorous convergence analysis is conducted showing that proposed method first-order convergent. Finally, two test examples used to validate theoretical findings.