Applying differential transformation method to the one-dimensional planar Bratu problem

2007 ◽  
Vol 2 ◽  
pp. 1493-1504 ◽  
Author(s):  
I. H. Abdel-Halim Hassan ◽  
V. S. Erturk
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
One Dimensional ◽  
Differential Transformation ◽  
The One ◽  
Bratu Problem

Numerical Multistep Approach for Solving Fractional Partial Differential Equations

2017 ◽  
Vol 14 (03) ◽  
pp. 1750029 ◽  
Author(s):  
Mohammed Al-Smadi ◽  
Asad Freihat ◽  
Hammad Khalil ◽  
Shaher Momani ◽  
Rahmat Ali Khan
Keyword(s):  
Fractional Derivatives ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Transformation Method ◽  
Time Frame ◽  
Differential Transformation Method ◽  
Heat Equations ◽  
One Dimensional ◽  
Analytical Technique ◽  
Differential Transformation

In this paper, we proposed a novel analytical technique for one-dimensional fractional heat equations with time fractional derivatives subjected to the appropriate initial condition. This new analytical technique, namely multistep reduced differential transformation method (MRDTM), is a simple amendment of the reduced differential transformation method, in which it is treated as an algorithm in a sequence of small intervals, in order to hold out accurate approximate solutions over a longer time frame compared to the traditional RDTM. The fractional derivatives are described in the Caputo sense, while the behavior of solutions for different values of fractional order [Formula: see text] compared with exact solutions is shown graphically. The analysis is accompanied by four test examples to demonstrate that the proposed approach is reliable, fully compatible with the complexity of these equations, and can be strongly employed for many other nonlinear problems in fractional calculus.

Differential transformation method for circular membrane vibrations

2020 ◽  
Vol 61(12) (2) ◽  
pp. 333-350
Author(s):  
Jaipong Kasemsuwan ◽  
◽  
Sorin Vasile Sabau ◽  
Uraiwan Somboon ◽  
◽  
...  
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
Circular Membrane ◽  
Differential Transformation ◽  
Membrane Vibrations

scholarly journals Differential Transformation Method (DTM) for Solving SIS and SI Epidemic Models

2017 ◽  
Vol 46 (10) ◽  
pp. 2007-2017
Author(s):  
M.Z. Ahmad ◽  
D. Alsarayreh ◽  
A. Alsarayreh ◽  
I. Qaralleh
Keyword(s):  
Transformation Method ◽  
Epidemic Models ◽  
Differential Transformation Method ◽  
Differential Transformation
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