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 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 Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

2016 ◽  
Vol 12 (8) ◽  
pp. 6530-6544
Author(s):  
Mohamed S M. Bahgat
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
Partial Differential ◽  
Adomian Decomposition

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components.

Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Jafari
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Decomposition Methods ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

scholarly journals On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers' Equation

2019 ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Adem Kilicman
Keyword(s):  
Laplace Transform ◽  
Burgers Equation ◽  
Decomposition Methods ◽  
Laplace Transforms ◽  
Existence Condition ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Coupled Burgers Equation

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

Sign in / Sign up

Export Citation Format

Share Document