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Title: A fully discrete ?-uniform method for convection-diffusion problem on equidistant meshes
Authors: Filiz, Ali
Neslitürk, Ali İhsan
Ekici, Mehmet
Keywords: ε-Uniform
Fitted operator method
Shishkin mesh
Singular perturbation
Issue Date: 2012
Publisher: Hikari Ltd.
Source: Filiz, A., Neslitürk, A. İ., and Ekici, M. (2012). A fully discrete ε-uniform method for convection-diffusion problem on equidistant meshes. Applied Mathematical Sciences, 6(17-20), 827-842.
Abstract: For a singularly-perturbed two-point boundary value problem, we propose an ε-uniform finite difference method on an equidistant mesh which requires no exact solution of a differential equation. We start with a full-fitted operator method reflecting the singular perturbation nature of the problem through a local boundary value problem. However, to solve the local boundary value problem, we employ an upwind method on a Shishkin mesh in local domain, instead of solving it exactly. We further study the convergence properties of the numerical method proposed and prove it nodally converges to the true solution for any ε.
ISSN: 1312-885X
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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