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

Year 2019, Volume: 22 Issue: 2, 443 - 451, 01.06.2019

Berat Karaagac Yusuf Ucar N. Murat Yagmurlu Alaattin Esen

https://doi.org/10.2339/politeknik.428986

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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