SOLVING DIFFERENTIAL EQUATIONS USING ADOMIAN DECOMPOSITION METHOD AND DIFFERENTIAL TRANSFORM METHOD

2018 ◽  
Vol 19 (4) ◽  
pp. 323-342
Author(s):  
T. P. Ungani ◽  
E. Matabane
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Differential Transform

Semi-analytical treatments of conjugate heat transfer

2012 ◽  
Vol 227 (3) ◽  
pp. 492-503 ◽  
Author(s):  
Mohammad Reza Hajmohammadi ◽  
Seyed Salman Nourazar ◽  
Ali Habibi Manesh
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Temperature Distribution ◽  
Decomposition Method ◽  
Conjugate Heat Transfer ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Differential Transform

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.

Numerical Comparison of Methods for Solving Boundary Layer Problems in Hydrodynamics

2013 ◽  
Vol 284-287 ◽  
pp. 508-512
Author(s):  
Shih Hsiang Chang
Keyword(s):  
Boundary Layer ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Numerical Comparison ◽  
Transform Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Differential Transform ◽  
Boundary Layer Problems

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.

scholarly journals Solving fuzzy $(1+ n)$-dimensional Burgers’ equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mawia Osman ◽  
Zengtai Gong ◽  
Altyeb Mohammed Mustafa ◽  
Hong Yang
Keyword(s):  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Differential Transform

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.

scholarly journals Application of Natural Transform Method to Fractional Pantograph Delay Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
M. Valizadeh ◽  
Y. Mahmoudi ◽  
F. Dastmalchi Saei
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
New Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Delay Differential

In this paper, a new method based on combination of the natural transform method (NTM), Adomian decomposition method (ADM), and coefficient perturbation method (CPM) which is called “perturbed decomposition natural transform method” (PDNTM) is implemented for solving fractional pantograph delay differential equations with nonconstant coefficients. The fractional derivative is regarded in Caputo sense. Numerical evaluations are included to demonstrate the validity and applicability of this technique.

Sign in / Sign up

Export Citation Format

Share Document