Sürdürülebilir Kalkınma Amaçları
Yayınlar
- MakaleYalnız künye2012A multistage differential transformation method for approximate solution of Hantavirus infection model
Gökdoĝan, 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.
- MakaleYalnız künye2012A multistage variational iteration method for approximateanalytic solution of avian-human influenza epidemic model
Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat
In this paper, the approximate solution of avian-human influenza epidemic model is obtained by a reliable algorithm based on an adaptation of the standard variational iteration method (VIM), which is called the multi-stage variational iteration method (MVIM). A comparison between MVIM and the Runge-Kutta method (RK-method) reveals that the proposed technique is a promising tool to solve the considered problem.
- MakaleAçık Erişim2012On the solutions fractional Riccati differential equation with modified Riemann-Liouville derivative
Merdan, Mehmet
Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. The behavior of the solutions and the effects of different values of fractional order α are indicated graphically. The results obtained by the FVIM reveal that the method is very reliable, convenient, and effective method for nonlinear differential equations with modified Riemann-Liouville derivative
- MakaleYalnız künye2012Numerical solution of time-fraction modified equal width wave equation
Merdan, Mehmet; Yildirim, Ahmet; Gökdoǧan, 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.
- MakaleAçık Erişim2012Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method
Merdan, Mehmet; Gökdogan, 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.
- MakaleAçık Erişim2012Adaptive multi-step differential transformation method to solving nonlinear differential equations
Gökdogan, 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.
- MakaleYalnız künye2011Numerical Approximations to Solution of Biochemical Reaction Model
Yildirim, Ahmet; Gökdogan, 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.
- MakaleAçık Erişim2011On the numerical solution of the model for HIV infection of CD4+ T cells
Merdan, Mehmet; Gökdogan, 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.
- MakaleAçık Erişim2011Solving a fractional order model of HIV infection of CD4+ T cells
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.
- MakaleAçık Erişim2011Solution of nonlinear oscillators with fractional nonlinearities by using the modified differential transformation method
Merdan, Mehmet; Gökdoǧan, Ahmet
In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. The reliability of this method is investigated by comparison with the classical fourth-order Runge-Kutta (RK4) method and Cos-AT and Sine-AT method. Our the presented method showed results to analytical solutions of nonlinear ordinary differential equation. Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods.
- MakaleYalnız künye2010Homotopy perturbation method for solving a three-species food chain model
Merdan, Mehmet
In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equa tion systems such as a three-species food chain model. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Padé approximants. Some plots are presented to show the reliability and simplicity of the methods.
- MakaleYalnız künye2010A new application of modified differential transformation method for modelling the pollution of a system of lakes
Merdan, Mehmet
In this papers, a new application of modified differential transformation method (MDTM) is implemented to solve analytically systems of nonlinear ordinary differential equations such as modelling the pollution of a system of lakes. The proposed scheme is based on differential transformation method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. The results are compared with the results obtained by MATLAB ode23s and the differential transformation method (DTM) are applied Padé approximants. At the end, these solutions are illustrated by tables and figures.
- MakaleAçık Erişim2009Homotopy perturbation method for solving human T-Cell lymphotropic virus I(HTLV-I) infection of CD4+ T-Cells model
Merdan, Mehmet
In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Padé approximants. The results to get the homotopy perturbation method (HPM) is applied Padé approximants. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. Some plots arepresented to show the reliability and simplicity of the methods.