A new parameter-uniform discretization of semilinear singularly perturbed problems

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2022

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MDPI

Abstract

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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Quasilinearization, Fluid dynamics, Quantum mechanics, Plasma dynamics, Aerodynamics

Citation

Munyakazi, J. B., & Kehinde, O. O. (2022). A new parameter-uniform discretization of semilinear singularly perturbed problems. Mathematics, 10(13), 2254. https://doi.org/10.3390/math10132254

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https://doi.org/10.3390/math10132254
 http://hdl.handle.net/10566/7889

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Research Articles (Mathematics)