Numerical solution of time fractional nonlinear Klein–Gordon equation using Sinc–Chebyshev collocation method

2017 ◽  
Vol 310 ◽  
pp. 139-148 ◽  
Author(s):  
A.M. Nagy
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals The numerical solution of the time-fractional non-linear Klein-Gordon equation via spectral collocation method

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1529-1537 ◽  
Author(s):  
Yin Yang ◽  
Xinfa Yang ◽  
Jindi Wang ◽  
Jie Liu
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Spectral Expansion ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
L2 Norm ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we consider the numerical solution of the time-fractional non-linear Klein-Gordon equation. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. A rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted L2-norm. Numerical tests are carried out to confirm the theoretical results.

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 A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Berna Bülbül ◽  
Mehmet Sezer
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Numerical Method ◽  
Error Estimation ◽  
Matrix Method ◽  
Gordon Equation ◽  
New Approach ◽  
Collocation Points ◽  
Klein Gordon ◽  
Klein Gordon Equation

A numerical method based on collocation points is developed to solve the nonlinear Klein-Gordon equations by using the Taylor matrix method. The method is applied to some test examples and the numerical results are compared with the exact solutions. The results reveal that the method is very effective, simple, and convenient. In addition, an error estimation of proposed method is presented.

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