scholarly journals The GDTM-Padé Technique for the Nonlinear Lattice Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Junfeng Lu
Keyword(s):  
Exact Solutions ◽  
Padé Approximation ◽  
High Accuracy ◽  
Numerical Results ◽  
Differential Transform Method ◽  
Pade Approximation ◽  
Transform Method ◽  
Differential Transform ◽  
Nonlinear Lattice ◽  
Generalized Differential

The GDTM-Padé technique is a combination of the generalized differential transform method and the Padé approximation. We apply this technique to solve the two nonlinear lattice equations, which results in the high accuracy of the GDTM-Padé solutions. Numerical results are presented to show its efficiency by comparing the GDTM-Padé solutions, the solutions obtained by the generalized differential transform method, and the exact solutions.

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 Comparing Numerical Methods for Solving Time-Fractional Reaction-Diffusion Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Veyis Turut ◽  
Nuran Güzel
Keyword(s):  
Fractional Derivatives ◽  
Padé Approximation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Pade Approximation ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential ◽  
Fractional Reaction

Multivariate Padé approximation (MPA) is applied to numerically approximate the solutions of time-fractional reaction-diffusion equations, and the numerical results are compared with solutions obtained by the generalized differential transform method (GDTM). The fractional derivatives are described in the Caputo sense. Two illustrative examples are given to demonstrate the effectiveness of the multivariate Padé approximation (MPA). The results reveal that the multivariate Padé approximation (MPA) is very effective and convenient for solving time-fractional reaction-diffusion equations.

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 the fractional nonlinear Bloch system using the multi-step generalized differential transform method

2014 ◽  
Vol 68 (12) ◽  
pp. 2124-2132 ◽  
Author(s):  
Eman Abuteen ◽  
Shaher Momani ◽  
Ahmad Alawneh
Keyword(s):  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential

scholarly journals Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

2020 ◽  
pp. 34-43
Author(s):  
Fadwa A. M. Madi ◽  
Fawzi Abdelwahid
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Linear Partial Differential Equations ◽  
Differential Transform ◽  
Non Linear

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

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