 A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layerJustin B. Munyakazi, Kailash C. Patidar and Mbani T. Sayi Mathematics and Computers in Simulation (MATCOM), 2019, vol. 160, issue C, 155-167 Abstract: The objectives of this paper are to construct and study a fitted operator finite difference method for the class of singularly perturbed problems whose solution exhibits an interior layer due to the presence of a turning point. We first establish sharp bounds on the solution and its derivatives. Then in line with other fitted operator methods that are designed in various recent works in numerical singular perturbation theory by the first two authors, we propose a fitted operator finite difference method to solve this interior layer problem. This method is then analysed by making use of the bounds on the solutions that we derive. We show that the scheme is uniformly convergent of order one. We also apply Richardson extrapolation as the acceleration technique to improve the accuracy and the order of convergence of the scheme up to two. Numerical investigations are carried out to demonstrate the efficacy and robustness of the scheme. Keywords: Singular perturbations; Turning point; Interior layer; Error bounds; Uniform convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:160:y:2019:i:c:p:155-167 DOI: 10.1016/j.matcom.2018.12.010 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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