A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems
Date
2022Author
Kehinde, Olawale O.
Munyakazi, Justin B.
Appadu, Appanah R.
Metadata
Show full item recordAbstract
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.