Robust numerical method for singularly perturbed semilinear parabolic differential difference equations

Masho Jima Kabeto and Gemechis File Duressa

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 188, issue C, 537-547

Abstract: This paper deals with the robust numerical method for solving the singularly perturbed semilinear partial differential equation with the spatial delay. The quadratically convergent quasilinearization technique is used to linearize the semilinear term. It is formulated by discretization of the solution domain and then replacing the differential equation by finite difference approximation that in turn gives the system of algebraic equations. The method is shown to be first-order convergent. It is observed that the convergence is independent of the perturbation parameter. Numerical illustrations are investigated on model examples to support the theoretical results and the effectiveness of the method.

Keywords: Singularly perturbed parabolic equations; Semilinear; Fitted mesh method; Accurate solution (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:188:y:2021:i:c:p:537-547

DOI: 10.1016/j.matcom.2021.05.005

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