ON THE STABILITY ANALYSIS OF THE TIME-FRACTIONAL VARIABLE ORDER KLEIN-GORDON EQUATION AND SOME NUMERICAL SIMULATIONS
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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. Numerical examples are also given for illustration.