Numerical Comparison of Methods for Solving Boundary Layer Problems in Hydrodynamics

2013 ◽  
Vol 284-287 ◽  
pp. 508-512
Author(s):  
Shih Hsiang Chang

This paper presents a numerical comparison between the differential transform method and the modified Adomian decomposition method for solving the boundary layer problems arising in hydrodynamics. The results show that the differential transform method and modified Adomian decomposition method are easier and more reliable to use in solving this type of problem and provides accurate data as compared with those obtained by other numerical methods.

Author(s):  
Mohammad Reza Hajmohammadi ◽  
Seyed Salman Nourazar ◽  
Ali Habibi Manesh

A new algorithm is proposed based on semi-analytical methods to solve the conjugate heat transfer problems. In this respect, a problem of conjugate forced-convective flow over a heat-conducting plate is modeled and the integro-differential equation occurring in the problem is solved by two lately-proposed approaches, Adomian decomposition method and differential transform method. The solution of the governing integro-differential equation for temperature distribution of the plate is handled more easily and accurately by implementing Adomian decomposition method/differential transform method rather than other traditional methods such as perturbation method. A numerical approach is also performed via finite volume method to examine the validity of the results for temperature distribution of the plate obtained by Adomian decomposition method/differential transform method. It is shown that the expressions for the temperature distribution in the plate obtained from the two methods, Adomian decomposition method and differential transform method, are the same and show closer agreement to the results calculated from numerical work in comparison with the expression obtained by perturbation method existed in the literature.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mawia Osman ◽  
Zengtai Gong ◽  
Altyeb Mohammed Mustafa ◽  
Hong Yang

AbstractIn this paper, we study the comparison of fuzzy differential transform method (FDTM), fuzzy Adomian decomposition method (FADM), fuzzy homotopy perturbation method (FHPM), and fuzzy reduced differential transform method (FRDTM) to obtain the solutions of fuzzy $(1 + n)$ ( 1 + n ) -dimensional Burgers’ equation under gH-differentiability. We have investigated many new results to solve the above problem, and the methods have been implemented. The four illustrative numerical examples are presented to demonstrate the effectiveness of the proposed methods and also to demonstrate the efficiency and simplicity of the ways they were developed and derived. The results also show that the methods are powerful mathematical tools for solving fuzzy $(1 + n)$ ( 1 + n ) -dimensional Burgers’ equation.


2017 ◽  
Vol 10 (02) ◽  
pp. 1750025
Author(s):  
Hooman Fatoorehchi ◽  
Hossein Abolghasemi ◽  
Laura Villafuerte ◽  
Reza Zarghami

A nonlinear model representing oxygen diffusion accompanied by the Michaelis–Menten consumption kinetics inside a spherical cell is solved analytically by the differential transform method (DTM) and the modified Adomian decomposition method (MADM). A perfect agreement between the literature data and the results from the proposed solutions is found. The advantages and drawbacks of the two approaches are discussed and their efficiencies are compared through a CPU-time analysis.


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