Yazar "Modanli, Mahmut" seçeneğine göre listele

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    A numerical solution for a telegraph equation
    (American Institute of Physics Inc., 2014) Ashyralyev, Allaberen; Modanli, Mahmut
    In this study, the initial value problem for a telegraph equation in a Hilbert space is considered. The stability estimate for the solution of this problem is given. A first and a second order of approximation difference schemes approximately solving the initial value problem are presented. The stability estimates for the solution of these difference schemes are given. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments. © 2014 AIP Publishing LLC.
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    An operator method for telegraph partial differential and difference equations
    (Springeropen, 2015) Ashyralyev, Allaberen; Modanli, Mahmut
    The Cauchy problem for abstract telegraph equations d(2)u(t)/dt(2) + alpha du(t)/dt + Au(t) + beta u(t) = f (t) (0 <= t <= T), u(0) = phi, u'(0) = psi in a Hilbert space H with the self-adjoint positive definite operator A is studied. Stability estimates for the solution of this problem are established. The first and second order of accuracy difference schemes for the approximate solution of this problem are presented. Stability estimates for the solution of these difference schemes are established. In applications, two mixed problems for telegraph partial differential equations are investigated. The methods are illustrated by numerical examples.
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    Crank-Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana-Baleanu Caputo derivative
    (Pergamon-Elsevier Science Ltd, 2019) Akgul, Ali; Modanli, Mahmut
    In this paper, the third order partial differential equation defined by Caputo fractional derivative with Atangana-Baleanu derivative has been investigated. The stability estimates are proved for the exact solution. Difference schemes for Crank-Nicholson finite difference scheme method is constructed. The stability of difference schemes for this problem is shown by Von Neumann method (Fourier analysis method). Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the technique. The reproducing kernel function for the problem has been found. (C) 2019 Elsevier Ltd. All rights reserved.
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    FINITE DIFFERENCE METHOD FOR THE FRACTIONAL ORDER PSEUDO TELEGRAPH INTEGRO-DIFFERENTIAL EQUATION
    (Czestochowa Univ Technology, Inst Mathematics, 2022) Modanli, Mahmut; Ozbag, Fatih; Akgulma, Ali
    The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order alpha.
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    Finite difference method for transmission dynamics of Contagious Bovine Pleuropneumonia
    (Amer Inst Mathematical Sciences-Aims, 2022) Kikpinar, Sait; Modanli, Mahmut; Akgul, Ali; Jarad, Fahd
    In this study, the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by finite difference method are presented. This model is made up of sensitive, exposed, vaccinated, infectious, constantly infected, and treated compartments. The model is studied by the finite difference method. Firstly, the finite difference scheme is constructed. Then the stability estimates are proved for this model. As a result, several simulations are given for this model on the verge of antibiotic therapy. From these figures, the supposition that 50% of infectious cattle take antibiotic therapy or the date of infection decrease to 28 days, 50% of susceptible obtain vaccination within 73 days.
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    Nonlocal boundary value problem for telegraph equations
    (Amer Inst Physics, 2015) Ashyralyev, Allaberen; Modanli, Mahmut
    In this work, the nonlocal boundary value problem for a telegraph equation in a Hilbert space is conceived. Stability estimates for the solution of this problem are obtained. The first and second order of accuracy difference schemes for the approximate solution of this problem are constructed. Stability estimates for the solution of these difference schemes are established. In implementations, two mixed problems for telegraph partial differential equations are investigated. The methods are showed by numerical experiments.
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    Numerical solution of fractional telegraph differential equations by theta-method
    (Springer Heidelberg, 2017) Modanli, Mahmut; Akgul, Ali
    Difference schemes for theta method are constructed. Theta method is used to deal with fractional telegraph differential equation defined by Caputo fractional derivative for different values of theta = 0.1, 0.5, 0.9 and fractional orders alpha = 0.05, 0.1, 0.5, 0.9, 0.95. The stability of difference schemes for this problem is proved by matrix method and the stability of the exact solution is also given. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.
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    On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method
    (Walter De Gruyter Gmbh, 2020) Modanli, Mahmut; Akgul, Ali
    The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders alpha = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.
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    On solutions of fractional order time varying linear dynamical systems model
    (Taylor and Francis Ltd., 2021) Modanli, Mahmut; Akgül, Ali
    In this paper, the linear and nonlinear fractional order time varying linear dynamical systems model has been studied. The homotopy perturbation method is used to find the approximation solution. The obtained approximation solution is effective which is close to the exact solution. The results showed that the method is effective and useful. This method produce better approximations than the ones produced with the standard weighted residual methods. Additionally, some useful reproducing kernel functions have been obtained. Solutions of the models can be obtained by the reproducing kernel method with these reproducing kernel functions. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
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    On Solutions of Fractional Telegraph Model With Mittag-Leffler Kernel
    (Asme, 2022) Akgul, Ali; Modanli, Mahmut
    In this paper, we research the fractional telegraph equation with the Atangana-Baleanu-Caputo derivative. We use the Laplace method to find the exact solution of the problems. We construct the difference schemes for the implicit finite method. We prove the stability of difference schemes for the problems by the matrix method. We demonstrate the accuracy of the method by some numerical experiments.
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    On solutions to the second-order partial differential equations by two accurate methods
    (Wiley, 2018) Modanli, Mahmut; Akgul, Ali
    In this article, we investigate the reproducing kernel method and the difference schemes method for solving the second-order partial differential equations. Numerical results have been shown to prove the efficiency of the methods. Results prove that the methods are very effective.
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    Two approximation methods for fractional order Pseudo-Parabolic differential equations
    (Elsevier, 2022) Modanli, Mahmut; Goktepe, Ecem; Akgul, Ali; Alsallami, Shami A. M.; Khalil, E. M.
    In this study, fractional order pseudo-parabolic partial differential equation defined by Caputo derivative is investigated with initial-boundary conditions. Modified double Laplace decomposition method is used to find the exact solution of this equation. Explicit finite difference is constructed for this partial differential equation. Stability estimates are proved for these difference schemes. Error analysis table is obtained by compared the exact and approximate solutions. Figures showing the physical properties of the exact and approximate solutions are presented. From the error tables and figures, this applied method is an good and effective method for this equation.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).