Yazar "Merdan, Mehmet" seçeneğine göre listele

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    Adaptive multi-step differential transformation method to solving nonlinear differential equations
    (Pergamon-Elsevier Science Ltd, 2012) Gokdogan, Ahmet; Merdan, Mehmet; Yildirim, Ahmet
    In this paper, we propose a fast and effective adaptive algorithm for the multi-step differential transformation method (MsDTM). This approach named as the adaptive MsDTM is applied to a number of nonlinear differential equations and numerical results are given. At the same time, a comparison between the MsDTM and the adaptive MsDTM reveals that the proposed approach is an efficiency tool for solving the considered equations using fewer time steps. (C) 2011 Elsevier Ltd. All rights reserved.
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    The modified algorithm for the differential transform method to solution of Genesio systems
    (Elsevier Science Bv, 2012) Gokdogan, Ahmet; Merdan, Mehmet; Yildirim, Ahmet
    In this article, approximate analytical solution of chaotic Genesio system is acquired by the modified differential transform method (MDTM). The differential transform method (DTM) is mentioned in summary. MDTM can be obtained from DTM applied to Laplace, inverse Laplace transform and Pade approximant. The MDTM is used to increase the accuracy and accelerate the convergence rate of truncated series solution getting by the DTM. Results are given with tables and figures. (C) 2011 Elsevier B.V. All rights reserved.
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    A multistage differential transformation method for approximate solution of Hantavirus infection model
    (Elsevier Science Bv, 2012) Gokdogan, Ahmet; Merdan, Mehmet; Yildirim, Ahmet
    The goal of this study is presented a reliable algorithm based on the standard differential transformation method (DTM), which is called the multi-stage differential transformation method (MsDTM) for solving Hantavirus infection model. The results obtanied by using MsDTM are compared to those obtained by using the Runge-Kutta method (R-K-method). The proposed technique is a hopeful tool to solving for a long time intervals in this kind of systems. (C) 2011 Elsevier B.V. All rights reserved.
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    Numerical Approximations to Solution of Biochemical Reaction Model
    (Berkeley Electronic Press, 2011) Yildirim, Ahmet; Gokdogan, Ahmet; Merdan, Mehmet
    In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.
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    Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method
    (Hindawi Publishing Corporation, 2012) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions.
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    Numerical solution of time-fraction modified equal width wave equation
    (Emerald Group Publishing Limited, 2012) Merdan, Mehmet; Yildirim, Ahmet; Gokdogan, Ahmet
    Purpose - The purpose of this paper is to show how an application of fractional two dimensional differential transformation method (DTM) obtained approximate analytical solution of time-fraction modified equal width wave (MEW) equation. Design/methodology/approach - The fractional derivative is described in the Caputo sense. Findings - It is indicated that the solutions obtained by the two dimensional DTM are reliable and that this is an effective method for strongly nonlinear partial equations. Originality/value - The paper shows that exact solutions can also be obtained from the known forms of the series solutions.
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    On numerical solution to fractional non-linear oscillatory equations
    (Springer, 2013) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet
    In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations. The results indicate that the method is very effective and sufficient for solving non-linear differential equations of fractional order.
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    On the numerical solution of the model for HIV infection of CD4(+) T cells
    (Pergamon-Elsevier Science Ltd, 2011) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet
    In this article, a variational iteration method (VIM) is performed to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as a model for HIV infection of CD4(+) T cells. A modified VIM (MVIM), based on the use of Fade approximants is proposed. Some plots are presented to show the reliability and simplicity of the methods. (C) 2011 Elsevier Ltd. All rights reserved.
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    Solution of time-fractional generalized Hirota-Satsuma coupled KdV equation by generalised differential transformation method
    (Emerald Group Publishing Ltd, 2013) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    Purpose - In this article, the aim is to obtain an approximate analytical solution of time-fraction generalized Hirota-Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions. Design/methodology/approach - Two dimensional differential transformation method (DTM) is used. Findings - In this paper, the fractional differential transformation method is implemented to the solution of time-fraction generalized generalized Hirota-Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. Originality/value - This is an original work in which the results indicate that the method is powerful and significant for solving time-fraction generalized generalized Hirota-Satsuma coupled KDV type differential equations.
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    Solution of time-fractional generalized Hirota-Satsuma coupled KdV equation by generalised differential transformation method
    (Emerald Group Publishing Ltd, 2013) Merdan, Mehmet; Gokdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef
    Purpose - In this article, the aim is to obtain an approximate analytical solution of time-fraction generalized Hirota-Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions. Design/methodology/approach - Two dimensional differential transformation method (DTM) is used. Findings - In this paper, the fractional differential transformation method is implemented to the solution of time-fraction generalized generalized Hirota-Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. Originality/value - This is an original work in which the results indicate that the method is powerful and significant for solving time-fraction generalized generalized Hirota-Satsuma coupled KDV type differential equations.
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    Solving a fractional order model of HIV infection of CD4(+) T cells
    (Pergamon-Elsevier Science Ltd, 2011) Gokdogan, Ahmet; Yildirim, Ahmet; Merdan, Mehmet
    In this paper, a multi-step differential transform method (MsDTM) is performed to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as a model for HIV infection of CD4(+) T cells. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of fractional differential equations. Some figures are presented to show the reliability and simplicity of the methods. (C) 2011 Elsevier Ltd. All rights reserved.