WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
The Chebyshev Collection Method for Solving Fractional Order Klein-Gordon Equation
Authors: , ,
Abstract: In this paper, we are implemented the Chebyshev spectral method for solving the non-linear fractional Klein-Gordon equation (FKGE). The fractional derivative is considered in the Caputo sense. We presented an approximate formula of the fractional derivative. The properties of the Chebyshev polynomials are used to re- duce FKGE to the solution of system of ordinary differential equations which solved by using the finite difference method. Special attention is given to study the convergence analysis and estimate an upper bound of the error of the derived formula. The numerical results of applying this method to FKGE show the simplicity and the efficiency of the proposed method.
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Keywords: Fractional Klein-Gordon equation, Caputo derivative, Chebyshev spectral method, Convergence analysis
Pages: 31-38
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #4