Asymptotics of a compact scheme for solving a superdiffusion equation with several variable delays

A superdiffusion equation with space-fractional Riesz derivatives and with several time delay variables is considered. Constructions of a fractional analog of a compact scheme with piecewise cubic interpolation and extrapolation by continuation are presented, which has the second order of smallness with respect to the time discretization step $\Delta$ and the fourth with respect to the space discretization step $h$. This method is basic for subsequent constructions. The order of the residual without interpolation of the method is studied. The coefficients of the expansion of the residual with respect to $\Delta$ are written out. An asymptotic expansion of the residual with piecewise cubic interpolation and extrapolation by continuation is also written out. An equation for the main term of the asymptotic expansion of the global error is given. Under certain assumptions, the validity of using the Richardson extrapolation procedure is substantiated. A corresponding method is constructed, which has the order of $O(\Delta^4 + h^4)$ in the energy norm. The result of numerical modeling for superdiffusion equation with two variable delays is presented. The result of numerical experiment fully correspond to theoretical conclusions about the orders of convergence.