Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Şendur, AliSubject: search.filters.subject.Singular perturbation

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  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    Finite Difference Approximations of Multidimensional Convection-Diffusion Problems With Small Diffusion on a Special Grid
    (Elsevier Ltd., 2015) Kaya, Adem; Şendur, Ali
    A numerical scheme for the convection-diffusion-reaction (CDR) problems is studied herein. We propose a finite difference method on a special grid for solving CDR problems particularly designed to treat the most interesting case of small diffusion. We use the subgrid nodes in the Link-cutting bubble (LCB) strategy [5] to construct a numerical algorithm that can easily be extended to the higher dimensions. The method adapts very well to all regimes with continuous transitions from one regime to another. We also compare the performance of the present method with the Streamline-upwind Petrov-Galerkin (SUPG) and the Residual-Free Bubbles (RFB) methods on several benchmark problems. The numerical experiments confirm the good performance of the proposed method.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    A Fully Discrete ?-Uniform Method for Singular Perturbation Problems on Equidistant Meshes
    (Taylor and Francis Ltd., 2012) Filiz, Ali; Neslitürk, Ali; Şendur, Ali
    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