scholarly journals Reduced Differential Transform Method for Thermoelastic Problem in Hyperbolic Heat Conduction Domain

2021 ◽  
Vol 26 (1) ◽  
pp. 76-87
Author(s):  
K.K. Chaudhari ◽  
C.S. Sutar
Keyword(s):  
Heat Conduction ◽  
Generalized Solution ◽  
Differential Transform Method ◽  
Thermoelastic Problem ◽  
Hyperbolic Heat Conduction ◽  
Transform Method ◽  
Differential Transform ◽  
In Series ◽  
Thermoelastic Field ◽  
Reduced Differential Transform Method

Abstract In the present study, we have applied the reduced differential transform method to solve the thermoelastic problem which reduces the computational efforts. In the study, the temperature distribution in a two-dimensional rectangular plate follows the hyperbolic law of heat conduction. We have obtained the generalized solution for thermoelastic field and temperature field by considering non-homogeneous boundary conditions in the x and y direction. Using this method one can obtain a solution in series form. The special case is considered to show the effectiveness of the present method. And also, the results are shown numerically and graphically. The study shows that this method provides an analytical approximate solution in very easy steps and requires little computational work.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

Application of Differential Transform Method to Heat Conduction in Tapered Fins

2001 ◽  
Vol 124 (1) ◽  
pp. 208-209 ◽  
Author(s):  
Charles W. Bert
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Special Functions ◽  
Differential Transform Method ◽  
Series Method ◽  
Transform Method ◽  
Differential Transform ◽  
Method Of Solution ◽  
Triangular Profile ◽  
Steady State Heat

This paper analyzes steady-state heat conduction in a triangular-profile fin using a relatively new, exact series method of solution known as the differential transform method. This method converges with only six terms or less for the cases considered. Its advantage is that, unlike many popular methods, it is an exact method and yet it does not require the use of Bessel or other special functions.

scholarly journals Solving a Higher-Dimensional Time-Fractional Diffusion Equation via the Fractional Reduced Differential Transform Method

2021 ◽  
Vol 5 (4) ◽  
pp. 168
Author(s):  
Salah Abuasad ◽  
Saleh Alshammari ◽  
Adil Al-rabtah ◽  
Ishak Hashim
Keyword(s):  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Differential Transform Method ◽  
Diffusion Equations ◽  
Caputo Fractional Derivatives ◽  
Transform Method ◽  
Fractional Diffusion Equations ◽  
Higher Dimensional ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.

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