Solution of the nonlinear Klein-Gordon equation for two new terms via the Adomian decomposition method

2014 ◽  
Vol 129 (2) ◽  
Author(s):  
H. Ghasemi ◽  
M. Ghovatmand ◽  
S. Zarrinkamar ◽  
H. Hassanabadi
Keyword(s):  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

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 Solutions of Klein-Gordon Equation by the Laplace Decomposition Method and Modified Laplace Decomposition Method

2021 ◽  
pp. 11-19
Author(s):  
R. M. Wayal
Keyword(s):  
Decomposition Method ◽  
Gordon Equation ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Initial Profile ◽  
Computational Work ◽  
Klein Gordon ◽  
Laplace Decomposition Method ◽  
Klein Gordon Equation ◽  
Good Agreement

In this article, the Laplace decomposition method and Modified Laplace decomposition method have been employed to obtain the exact and approximate solutions of the Klein-Gordon equation with the initial profile. An approximate solution obtained by these methods is in good agreement with the exact solution and shows that these approaches can solve linear and nonlinear problems very effectively and are capable to reduce the size of computational work.

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