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.

scholarly journals Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings

2019 ◽  
Vol 3 (2) ◽  
pp. 26 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Kamil Jassim
Keyword(s):  
Wave Equation ◽  
Decomposition Method ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Damped Wave Equation ◽  
Fractal Strings ◽  
Fractional Derivative Operators ◽  
Laplace Decomposition Method ◽  
Dissipative Wave Equation

In this paper, we apply the local fractional Laplace variational iteration method (LFLVIM) and the local fractional Laplace decomposition method (LFLDM) to obtain approximate solutions for solving the damped wave equation and dissipative wave equation within local fractional derivative operators (LFDOs). The efficiency of the considered methods are illustrated by some examples. The results obtained by LFLVIM and LFLDM are compared with the results obtained by LFVIM. The results reveal that the suggested algorithms are very effective and simple, and can be applied for linear and nonlinear problems in sciences and engineering.

Approximate Solutions of D-Dimensional Klein-Gordon Equation with modified Hylleraas Potential

2013 ◽  
Vol 54 (11) ◽  
pp. 2041-2051 ◽  
Author(s):  
Akpan N. Ikot ◽  
Oladunjoye A. Awoga ◽  
Akaninyene D. Antia ◽  
Hassan Hassanabadi ◽  
Elham Maghsoodi
Keyword(s):  
Gordon Equation ◽  
Approximate Solutions ◽  
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 Approximate solutions to the nonlinear Klein-Gordon equation in de Sitter spacetime

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 314-320 ◽  
Author(s):  
Muhammet Yazici ◽  
Süleyman Şengül
Keyword(s):  
Gordon Equation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Initial Value ◽  
Transform Method ◽  
Sitter Spacetime ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractWe consider initial value problems for the nonlinear Klein-Gordon equation in de Sitter spacetime. We use the differential transform method for the solution of the initial value problem. In order to show the accuracy of results for the solutions, we use the variational iteration method with Adomian’s polynomials for the nonlinearity. We show that the methods are effective and useful.

scholarly journals Approximate Solutions of Klein-Gordon Equation with Kratzer Potential

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
H. Hassanabadi ◽  
H. Rahimov ◽  
S. Zarrinkamar
Keyword(s):  
Gordon Equation ◽  
Approximate Solutions ◽  
Ansatz Method ◽  
Energy Behavior ◽  
Klein Gordon ◽  
Klein Gordon Equation

Approximate solutions of theD-dimensional Klein-Gordon equation are obtained for the scalar and vector general Kratzer potential for anylby using the ansatz method. The energy behavior is numerically discussed.

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