Gökdoǧan, Ahmet; Merdan, Mehmet

In this paper, it is given a fast algorithm to solve chaotic differential systems using the multi-step differential transforms method (MsDTM). The approach is applied to a number of chaotic nonlinear differential equations and numerical results are given. Performance analyses reveal that the proposed approach is an efficiency tool to solve using fewer time step to the considered equation systems.

Merdan, Mehmet; Gökdoǧan, 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.

Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat

In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.

Yildirim, Ahmet; Gökdoǧan, Ahmet; Merdan, Mehmet

In this article, the multi-step differential transform method is implemented to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems, such as Chen, Lorenz, Arneodo-Coullet, Genesio, Lui, and Rikitake chaotic systems. The numerical solutions obtained from the proposed method indicate that the approach is easy, simple, and accurate when applied to systems of fractional differential equations. Numerical simulations are given to verify the reliability and effectiveness of this method.

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.

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.

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.