Generalized Differential Transform Method for Solving Discrete Complex Cubic Ginzburg–Landau Equation

2015 ◽  
Vol 12 (03) ◽  
pp. 1550017 ◽  
Author(s):  
H. Aminikhah ◽  
P. Dehghan
Keyword(s):  
Solitary Wave Solution ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Differential Transform Method ◽  
Transform Method ◽  
Ginzburg Landau ◽  
Differential Transform ◽  
Generalized Differential ◽  
Discrete Complex

In this paper, generalized differential transform method (GDTM) is applied to solve discrete complex cubic Ginzburg–Landau (DCCGL) equation which is a famous nonlinear difference-differential equation (NDDE). GDTM approximate solutions for various discrete soliton solutions of DCCGL such as discrete bright soliton, discrete dark soliton, and discrete alternating soliton are obtained. Also this method is successfully employed to obtain approximate solution for dark solitary wave solution of integrable discrete nonlinear Schrödinger (IDNS) equation. Numerical results compared with their corresponding numerical and analytical solutions to show the efficiency and high accuracy of the considered method.

scholarly journals Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shaher Momani ◽  
Asad Freihat ◽  
Mohammed AL-Smadi
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense. Furthermore, we present figurative comparisons between the proposed scheme and the classical fourth-order Runge-Kutta method to demonstrate the accuracy and applicability of this method. The graphical results reveal that only few terms are required to deduce the approximate solutions which are found to be accurate and efficient.

Analytical Approach to Time-Fractional Partial Differential Equations in Fluid Mechanics

2011 ◽  
Vol 347-353 ◽  
pp. 463-466
Author(s):  
Xue Hui Chen ◽  
Liang Wei ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential

The generalized differential transform method is implemented for solving time-fractional partial differential equations in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor’s formula. Results obtained by using the scheme presented here agree well with the numerical results presented elsewhere. The results reveal the method is feasible and convenient for handling approximate solutions of time-fractional partial differential equations.

scholarly journals Solving time-fractional chemical engineering equations by generalized differential transform method

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 157-164
Author(s):  
Ahmad Haghbin ◽  
Hossein Jafari ◽  
Pranay Goswami ◽  
Morganathan Ariyan
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Convergent Series ◽  
High Accuracy ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.

scholarly journals Solving time-fractional chemical engineering equations by generalized differential transform method

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 157-164
Author(s):  
Ahmad Haghbin ◽  
Hossein Jafari ◽  
Pranay Goswami ◽  
Morganathan Ariyan
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Convergent Series ◽  
High Accuracy ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.

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