Approximate Solution of Non-Linear Fractional Klein-Gordon Equation Using Spectral Collocation Method

Rubayyi T. Alqahtani

Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.

DOI: 10.4236/am.2015.613190                

Abstract

In this paper, we implement the spectral collocation method with the help of the Legendre poly-nomials for solving the non-linear Fractional (Caputo sense) Klein-Gordon Equation (FKGE). We present an approximate formula of the fractional derivative. The Legendre collocation method is used to reduce FKGE to the solution of system of ODEs which is solved by using finite difference method. The results of applying the proposed method to the non-linear FKGE show the simplicity and the efficiency of the proposed method.

Keywords

Fractional Klein-Gordon Equation, Legendre Spectral Method

Conflicts of Interest

The authors declare no conflicts of interest.

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