A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation

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Politeknik Dergisi
Volume:22 Issue:2
A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation

A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation

Authors : Berat KARAAGAC, Yusuf UCAR, N Murat YAGMURLU, Alaattin ESEN

Pages : 443-451

Doi:10.2339/politeknik.428986

View : 29 | Download : 10

Publication Date : 2019-06-01

Article Type : Research Paper

Abstract :In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm. The fractional derivative in the given equation is handled in terms of Caputo sense. Using the methods, fractional differential equation is converted into algebraic equation system that are appropriate for computer coding. Then, two model problems are considered and their error norms are calculated to demonstrate the reliability and efficiency of the proposed method. The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.
Keywords : Finite element method, collocation, Fractional Klein Gordon equation, Caputo derivative

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