A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
Frontiers Media
Abstract
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.
Description
Keywords
Quasilinearization, Mathematics, Equations, Semilinear
Citation
Kehinde, O. O. et al. (2022). A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems. Frontiers in Applied Mathematics and Statistics, 8, 861276. 10.3389/fams.2022.861276