Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/4807
Title: A fully discrete ?-uniform method for singular perturbation problems on equidistant meshes
Authors: Filiz, Ali
Neslitürk, Ali
Şendur, Ali
Keywords: Finite differences
Fitted operator method
Shishkin mesh
Singular perturbation
Uniform convergence
Issue Date: Jan-2012
Publisher: Taylor and Francis Ltd.
Source: Filiz, A., Neslitürk, A., and Şendur, A. (2012). A fully discrete ε-uniform method for singular perturbation problems on equidistant meshes. International Journal of Computer Mathematics, 89(2), 190-199. doi:10.1080/00207160.2011.632411
Abstract: We propose a fully discrete ε-uniform finite-difference method on an equidistant mesh for a singularly perturbed two-point boundary-value problem (BVP). We start with a fitted operator method reflecting the singular perturbation nature of the problem through a local BVP. However, to solve the local BVP, we employ an upwind method on a Shishkin mesh in local domain, instead of solving it exactly. Thus, we show that it is possible to develop a ε-uniform method, totally in the context of finite differences, without solving any differential equation exactly. We further study the convergence properties of the numerical method proposed and prove that it nodally converges to the true solution for any ε. Finally, a set of numerical experiments is carried out to validate the theoretical results computationally. © 2012 Copyright Taylor and Francis Group, LLC
URI: http://doi.org/10.1080/00207160.2011.632411
http://hdl.handle.net/11147/4807
ISSN: 0020-7160
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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