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Browsing by Author "Cen, Zhongdi"

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    Article
    An Almost Second Order Uniformly Convergent Scheme for a Singularly Perturbed Initial Value Problem
    (Springer, 2014) Cen, Zhongdi; Erdogan, Fevzi; Xu, Aimin
    In this paper a nonlinear singularly perturbed initial problem is considered. The behavior of the exact solution and its derivatives is analyzed, and this leads to the construction of a Shishkin-type mesh. On this mesh a hybrid difference scheme is proposed, which is a combination of the second order difference schemes on the fine mesh and the midpoint upwind scheme on the coarse mesh. It is proved that the scheme is almost second-order convergent, in the discrete maximum norm, independently of singular perturbation parameter. Numerical experiment supports these theoretical results.
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    Article
    A Uniformly Almost Second Order Convergent Numerical Method for Singularly Perturbed Delay Differential Equations
    (Elsevier Science Bv, 2018) Erdogan, Fevzi; Cen, Zhongdi
    The purpose of this paper is to present a uniform finite difference method for the numerical solution of a second order singularly perturbed delay differential equation. The problem is solved by using a hybrid difference scheme on a Shishkin-type mesh. The method is shown to be uniformly convergent with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically. (C) 2017 Elsevier B.V. All rights reserved.