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Browsing by Author "Ekinci, Yilmaz"

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    Article
    A Numerical Approach for Solving Nonlinear Fredholm Integro-Differential Equation With Boundary Layer
    (Springer Heidelberg, 2022) Cakir, Musa; Ekinci, Yilmaz; Cimen, Erkan
    The study deals with an initial-value problem for a singularly perturbed nonlinear Fredholm integro-differential equation. Parameter explicit theoretical bounds on the continuous solution and its derivative are derived. To solve the approximate solution to this problem, a new difference scheme is constructed with the finite difference method by using the interpolated quadrature rules with the remaining terms in integral form. Parameter uniform error estimates for the approximate solution are established. It is proved that the method converges in the discrete maximum norm, uniformly with respect to the perturbation parameter. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
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    Article
    Numerical Method for a Neutral Delay Differential Problem
    (Lebanese Univ, 2017) Cimen, Erkan; Ekinci, Yilmaz
    In this paper, the initial-value problem for a linear first order neutral delay differential equation is considered. To solve this problem numerically, we construct a fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. Also, the method is first-order convergent in the discrete maximum norm. Furthermore, numerical illustrations provide support of the theoretical results.