Browsing by Author "Erdogan, Fevzi"

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    A fitted numerical method for singularly perturbed integro differential equations with delay
    (Видавництво Львівської політехніки, 2017-12-23) Erdogan, Fevzi; Sakar, Mehmet Giyas; Yuzuncu Yil University, Faculty of Sciences, Department of Mathematics, Van, Turkey
    This study deals with the singularly perturbed initial value problems for a quasilinear first-order integrodifferential equations with delay. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the discrete solutions are uniformly convergent with respect to the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.
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    Exponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equations
    (Lviv Polytechnic Publishing House, 2016) Erdogan, Fevzi; Yuzuncu Yil University
    The purpose of this study is to present a uniform finite difference method for numerical solution of a initial value problem for quasi-linear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.
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    Numerical solution of singularlyperturbed convection-diffusion equations
    (Видавництво Львівської політехніки, 2017-12-23) Sakar, Mehmet Giyas; Erdogan, Fevzi; Yuzuncu Yil University, Faculty of Sciences, Department of Mathematics, Van, Turkey
    In this paper, a new method is given for solving singularly perturbed convection-diffusion problems. The present method is based on combining the asymptotic expansion method and the variational iteration method (VIM) with an auxiliary parameter. Numerical results show that the present method can provide very accurate numerical solutions not only in the boundary layer, but also away from the layer.