Sürdürülebilir Kalkınma Amaçları
Yayınlar
- MakaleYalnız künye2013Solution of time-fractional generalized Hirota-Satsuma coupled KdV equation by generalised differential transformation method
Merdan, Mehmet; Gökdogan, 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.
- MakaleYalnız künye2012Coupling of homotopy perturbation, Laplace transform and Padé approximants for nonlinear oscillatory systems
Merdan, Mehmet; Yildirim, Ahmet; Gökdogan, Ahmet; Mohyud-Din, Syed Tauseef
In this article, homotopy perturbation method coupled with Laplace transform and Padé 0approximants is applied on the re-formulated nonlinear oscillatory systems. Numerical results and graphical represenations explicitly reveal the complete reliability and effeicincy of the suggested algorithm.
- 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.