Exact solutions to one dimensional non-homogeneous parabolic problems by the homogeneous Adomian decomposition method

2007 ◽  
Vol 186 (2) ◽  
pp. 969-979 ◽  
Author(s):  
Bongsoo Jang
Keyword(s):  
Exact Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Parabolic Problems ◽  
One Dimensional ◽  
Adomian Decomposition

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals A Note on Conformable Double Laplace Transform and Singular Conformable Pseudoparabolic Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Pseudoparabolic Equation ◽  
New Approach ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Pseudoparabolic Equations

In this work, we combine conformable double Laplace transform and Adomian decomposition method and present a new approach for solving singular one-dimensional conformable pseudoparabolic equation and conformable coupled pseudoparabolic equation. Furthermore, some examples are given to show the performance of the proposed method.

scholarly journals Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

2020 ◽  
Vol 52 (3) ◽  
pp. 339-352
Author(s):  
Omar Saber Qasim ◽  
Karam Adel Abed ◽  
Ahmed F. Qasim
Keyword(s):  
Exact Solutions ◽  
Hybrid Method ◽  
Decomposition Method ◽  
Firefly Algorithm ◽  
Fitness Function ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Optimal Parameters ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.

Fractional One-Dimensional Transport Equation Within Spectral Method Combined With Modified Adomian Decomposition Method

2009 ◽  
Author(s):  
Dumitru Baleanu ◽  
Abdelouahab Kadem
Keyword(s):  
Transport Equation ◽  
Spectral Method ◽  
Chebyshev Polynomials ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Plane Geometry ◽  
One Dimensional ◽  
Dimensional Plane ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper the Chebyshev polynomials technique combined with the modified Adomian decomposition method were applied to solve analytically the fractional transport equation in one-dimensional plane geometry.

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