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An accurate numerical method for solving the linear fractional Klein–Gordon equation
Author(s) -
Khader M.M.,
Kumar Sunil
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3035
Subject(s) - mathematics , convergence (economics) , fractional calculus , klein–gordon equation , numerical analysis , chebyshev filter , ode , derivative (finance) , finite difference method , chebyshev iteration , mathematical analysis , nonlinear system , physics , quantum mechanics , financial economics , economics , economic growth
In this article, an implementation of an efficient numerical method for solving the linear fractional Klein–Gordon equation (LFKGE) is introduced. The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Chebyshev approximations and finite difference method (FDM). The proposed method reduces LFKGE to a system of ODEs, which is solved using FDM. Special attention is given to study the convergence analysis and deduce an error upper bound of the proposed method. Numerical example is given to show the validity and the accuracy of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.