scholarly journals A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Murat Osmanoglu ◽  
Mustafa Bayram
Keyword(s):  
Numerical Method ◽  
Differential Algebraic Equations ◽  
Differential Transform Method ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Partial Differential Algebraic Equations ◽  
Differential Transform

scholarly journals Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Brahim Benhammouda ◽  
Hector Vazquez-Leal ◽  
Arturo Sarmiento-Reyes
Keyword(s):  
Perturbation Parameter ◽  
Convergent Series ◽  
Differential Algebraic Equations ◽  
Differential Transform Method ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Partial Differential Algebraic Equations ◽  
Differential Transform ◽  
Reduced Differential Transform Method

This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.

scholarly journals Analytical and approximate solutions of Fractional Partial Differential-Algebraic Equations

2020 ◽  
Vol 5 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Hatıra Günerhan ◽  
Ercan Çelik
Keyword(s):  
Numerical Solution ◽  
Approximate Solutions ◽  
Differential Algebraic Equations ◽  
Differential Transform Method ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Partial Differential Algebraic Equations ◽  
Differential Transform ◽  
Fractional Differential

AbstractIn this paper, we have extended the Fractional Differential Transform method for the numerical solution of the system of fractional partial differential-algebraic equations. The system of partial differential-algebraic equations of fractional order is solved by the Fractional Differential Transform method. The results exhibit that the proposed method is very effective.

scholarly journals A fuzzy solution of nonlinear partial differential equations

2021 ◽  
Vol 5 (1) ◽  
pp. 51-63
Author(s):  
Mawia Osman ◽  
◽  
Zengtai Gong ◽  
Altyeb Mohammed Mustafa ◽  
◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Infinite Series ◽  
Nonlinear Partial Differential Equations ◽  
Differential Transform Method ◽  
Series Expansions ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Fuzzy Solution

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

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