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

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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