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Browsing by Author "Durmaz, Muhammet Enes"

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    Article
    Numerical Solution of Singularly Perturbed Fredholm Integro-Differential Equations by Homogeneous Second Order Difference Method
    (Elsevier, 2022) Durmaz, Muhammet Enes; Cakir, Musa; Amirali, Ilhame; Amiraliyev, Gabil M.
    This work presents a computational approximate to solve singularly perturbed Fredholm integro-differential equation with the reduced second type Fredholm equation. This problem is discretized by a finite difference approximate, which generates second-order uniformly convergent numerical approximations to the solution. Parameter-uniform approximations are generated using Shishkin type meshes. The performance of the numerical scheme is tested which supports the effectiveness of the technique. (c) 2022 Elsevier B.V. All rights reserved.
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    Article
    Parameter Uniform Second-Order Numerical Approximation for the Integro-Differential Equations Involving Boundary Layers
    (Ankara Univ, Fac Sci, 2022) Durmaz, Muhammet Enes; Cakir, Musa; Amirali, Gabil
    The work handles a Fredholm integro-differential equation involv-ing boundary layers. A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions. The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.