A New Parameter-Uniform Discretization of Semilinear Singularly Perturbed Problems

Justin B. Munyakazi and Olawale O. Kehinde
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Justin B. Munyakazi: Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
Olawale O. Kehinde: Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa

Mathematics, 2022, vol. 10, issue 13, 1-14

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.

Keywords: singularly perturbed problems; semilinear differential equation; quasilinearization; boundary layer; fitted operator finite difference method; uniform convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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