On the stability analysis of the time-fractional variable order Klein-Gordon equation and a numerical simulation

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:69 Issue:1
On the stability analysis of the time-fractional variable order Klein-Gordon equation and a numerica...

On the stability analysis of the time-fractional variable order Klein-Gordon equation and a numerical simulation

Authors : Sinan DENİZ

Pages : 981-992

Doi:10.31801/cfsuasmas.450209

View : 35 | Download : 7

Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :In this paper, the Klein - Gordon equation is generalized using the concept of the variational order derivative. We try to construct the Crank-Nicholson scheme for numerical solutions of the modified Klein- Gordon equation. Stability analysis of the Crank-Nicholson scheme is examined and analyzed to prove the proposed method is stable for solving the time-fractional variable order Klein- Gordon equation. A numerical example is also given for illustration.
Keywords : Klein Gordon equation, fractional variable order derivative, Crank Nicholson scheme

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