Analysis of the Difference Scheme of Wave Equation Equivalent with Fractional Differentiation Operator

Analysis of the difference scheme of boundary-value problem for the wave equation analogue is in the paper. Explicit and implicit difference schemes for numerical solution of the Caputo initial boundary-value problem of the analogue for the wave equation with fractional differentiation operator are invest gated, and the criteria of these difference schemes sustainability have been proved by the harmonic Fourier method. Estimations for Eigen values of the operator transition from one time layer to another are obtained. Computational experiment on the analysis of the given difference scheme has been performed on the basis of example graphs of the numerical solution of the boundary-value problem for the wave equation with the operator of fractional differentiation having different values of parameters of fractional differentiation $\alpha$ and $\beta$ have been built. Change of the period of fluctuations upon transition to a fractional derivative is established. On an example it is shown that parameters $\alpha$ and $\beta$ become managing directors.