Generalized differential transform method to differential-difference equation

2009 ◽  
Vol 373 (45) ◽  
pp. 4142-4151 ◽  
Author(s):  
Li Zou ◽  
Zhen Wang ◽  
Zhi Zong
Keyword(s):  
Difference Equation ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Differential Difference Equation ◽  
Generalized Differential

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.

scholarly journals Application of the Multistep Generalized Differential Transform Method to Solve a Time-Fractional Enzyme Kinetics

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Alawneh
Keyword(s):  
Enzyme Kinetics ◽  
Fractional Derivatives ◽  
Differential Transform Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Kutta Method ◽  
Transform Method ◽  
Enzyme Substrate ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

The multistep differential transform method is first employed to solve a time-fractional enzyme kinetics. This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The results demonstrate reliability and efficiency of the algorithm developed.

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