Browsing by Author "Kehinde, Olawale O."

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    A new parameter-uniform discretization of semilinear singularly perturbed problems
    (MDPI, 2022) Munyakazi, Justin B.; Kehinde, Olawale O.
    In this paper, we present a numerical approach to solving singularly perturbed semilinear convection-diffusion problems. The nonlinear part of the problem is linearized via the quasilinearization technique. We then design and implement a fitted operator finite difference method to solve the sequence of linear singularly perturbed problems that emerges from the quasilinearization process. We carry out a rigorous analysis to attest to the convergence of the proposed procedure and notice that the method is first-order uniformly convergent. Some numerical evaluations are implemented on model examples to confirm the proposed theoretical results and to show the efficiency of the method.
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    A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems
    (Frontiers Media, 2022) Kehinde, Olawale O.; Munyakazi, Justin B.; Appadu, Appanah R.
    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.