Yazar "Inc, Mustafa" seçeneğine göre listele

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    Approximate solutions for MHD squeezing fluid flow by a novel method
    (Springer International Publishing Ag, 2014) Inc, Mustafa; Akgul, Ali
    In this paper, a steady axisymmetric MHD flow of two-dimensional incompressible fluids has been investigated. The reproducing kernel Hilbert space method (RKHSM) has been implemented to obtain a solution of the reduced fourth-order nonlinear boundary value problem. Numerical results have been compared with the results obtained by the Runge-Kutta method (RK-4) and optimal homotopy asymptotic method (OHAM).
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    Explicit Solution of Telegraph Equation Based on Reproducing Kernel Method
    (Hindawi Ltd, 2012) Inc, Mustafa; Akgul, Ali; Kilicman, Adem
    We propose a reproducing kernel method for solving the telegraph equation with initial conditions based on the reproducing kernel theory. The exact solution is represented in the form of series, and some numerical examples have been studied in order to demonstrate the validity and applicability of the technique. The method shows that the implement seems easy and produces accurate results.
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    Improved (G?/G)-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations
    (Hindawi Ltd, 2013) Akgul, Ali; Kilicman, Adem; Inc, Mustafa
    The fractional complex transformation is used to transform nonlinear partial differential equations to nonlinear ordinary differential equations. The improved (G'/G)-expansion method is suggested to solve the space and time fractional foam drainage and KdV equations. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
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    A New Application of the Reproducing Kernel Hilbert Space Method to Solve MHD Jeffery-Hamel Flows Problem in Nonparallel Walls
    (Hindawi Publishing Corporation, 2013) Inc, Mustafa; Akgul, Ali; Kilicman, Adem
    The present paper emphasizes Jeffery-Hamel flow: fluid flow between two rigid plane walls, where the angle between them is 2 alpha. A new method called the reproducing kernel Hilbert space method (RKHSM) is briefly introduced. The validity of the reproducing kernel method is set by comparing our results with HAM, DTM, and HPM and numerical results for different values of H, alpha, and Re. The results show up that the proposed reproducing kernel method can achieve good results in predicting the solutions of such problems. Comparison between obtained results showed that RKHSM is more acceptable and accurate than other methods. This method is very useful and applicable for solving nonlinear problems.
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    A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
    (Hindawi Ltd, 2013) Inc, Mustafa; Akgul, Ali; Kilicman, Adem
    We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.
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    Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method
    (Hindawi Ltd, 2013) Inc, Mustafa; Akgul, Ali; Kilicman, Adem
    We investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the form of a series in reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of this method. The results obtained from this method are compared with the exact solutions and other methods. Results of numerical examples show that this method is simple, effective, and easy to use.
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    Reproducing Kernel Hilbert Space Method for Solving Bratu's Problem
    (Springer, 2015) Inc, Mustafa; Akgul, Ali; Geng, Fazhan
    In this paper, we use the reproducing kernel Hilbert space method for solving a boundary value problem for the second order Bratu's differential equation. Convergence analysis of presented method is discussed. The numerical approximations to the exact solution are computed and compared with other existing methods. Our presented method produces more accurate results in comparison with those obtained by Adomian decomposition, Laplace decomposition, B-spline, non-polynomial spline and Lie-group shooting methods. Our yardstick is absolute error. The comparison of the results with exact ones is made to confirm the validity and efficiency.