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.

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 On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers’ Equation

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 417 ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Adem Kılıçman
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Existence Condition ◽  
New Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method ◽  
Coupled Burgers Equation

In the present work we introduced a new method and name it the conformable double Laplace decomposition method to solve one dimensional regular and singular conformable functional Burger’s equation. We studied the existence condition for the conformable double Laplace transform. In order to obtain the exact solution for nonlinear fractional problems, then we modified the double Laplace transform and combined it with the Adomian decomposition method. Later, we applied the new method to solve regular and singular conformable fractional coupled Burgers’ equations. Further, in order to illustrate the effectiveness of present method, we provide some examples.

scholarly journals Three-Dimensional Laplace Adomian Decomposition Method and Singular Pseudoparabolic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hassan Eltayeb ◽  
Diaa Eldin Elgezouli ◽  
Adem Kilicman ◽  
Imed Bachar
Keyword(s):  
Approximate Solution ◽  
Numerical Analysis ◽  
Decomposition Method ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Two Dimensional ◽  
Pseudoparabolic Equation ◽  
Adomian Decomposition ◽  
Pseudoparabolic Equations

In this work, the solution of the linear, nonlinear, and coupled system fractional singular two-dimensional pseudoparabolic equation is examined by using a three-dimensional Laplace Adomian decomposition method (3-DLADM). Analysis of the method is discussed, and some demonstrative examples are mentioned to confirm the power and accuracy of the recommended method, and numerical analysis is applied to sketch the exact and approximate solution.

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.

scholarly journals Solusi Persamaan Transport dengan Menggunakan Metode Dekomposisi Adomian Laplace

2020 ◽  
Vol 2 (2) ◽  
pp. 173
Author(s):  
Wahidah Sanusi ◽  
Syafruddin Side ◽  
Beby Fitriani
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Transport Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Inverse Laplace Transform ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Calculation Results

Abstrak. Penelitian ini mengkaji terbentuknya persamaan Transport dan menerapkan metode Dekomposisi Adomian Laplace dalam menentukan solusi persamaan Transport. Persamaan transport merupakan salah satu bentuk dari persamaan diferensial parsial. Bentuk umum persamaan Transport yaitu: Metode Dekomposisi Adomian Laplace merupakan kombinasi antara dua metode yaitu  metode dekomposisi adomian dan transformasi laplace. Penyelesaian persamaan Transport dengan metode Dekomposisi Adomian Laplace dilakukan dengan cara menggunakan tranformasi Laplace, mensubstitusi nilai awal, menyatakan solusi dalam bentuk deret tak hingga dan menggunakan invers transformasi laplace . Metode ini juga merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata Kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan Transport.This research discusses the solving of Transport equation applying Laplace Adomian Decomposition Method. Transport equation is one form of partial differential equations. General form of Transport equation is: Laplace Adomian Decomposition Method that combine between Laplace transform and Adomian Decomposition Method. The steps used to solve Transport equation are applying Laplace transform, initial value substitution, defining a solution as infinite series, then using the inverse Laplace transform. This method is a semi analytical method to solve for nonlinear ordinary differential equation. Based on the calculation results, the Laplace Adomian decomposition method can solve the solution of nonlinear ordinary differential equation.Keywords: Laplace Adomian Decomposition Method, Partial Differential Equation, Transport Equation.

NEW APPROACH OF THE ADOMIAN DECOMPOSITION METHOD

2017 ◽  
Vol 16 (1) ◽  
pp. 1-10
Author(s):  
Yaya Moussa ◽  
Youssouf Pare ◽  
Pierre Clovis Nitiema ◽  
Blaise Some
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
New Approach ◽  
Adomian Decomposition
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