Convergence of the high accuracy method for solving the nonlinear superdiffusion equation with functional delay

In this paper, the nonlinear superdiffusion equation with functional delay is considered. The discretization of the problem is performed. Constructions of the high accuracy difference method with piecewise linear interpolation are given. The order of the residual of the numerical method is studied. Under certain assumptions, the convergence of the second order in spatial and temporal steps and stability of the method is proved. The results of numerical experiments on test examples are presented.