Vladimir Pimenov, Ekaterina Tashirova

Convergence of Alikhanov's Method for Fractional Diffusion Equation with Drift and Functional Delay

abstract:
In this paper, a second-order method in time and space steps is constructed for a fractional diffusion equation in the presence of drift and functional delay. The basis of the algorithm is Alikhanov's method. To take into account the effect of functional delay, the interpolation and extrapolation constructions are used. The local error of the method is investigated. Using the discrete Gronwall inequality and some additional estimates, the convergence of the method is proved and the orders of convergence with respect to the partitioning steps in time and space are obtained. The results of numerical experiments on test examples are presented.

Mathematics Subject Classification: 65N06, 65N15, 65Q20

Key words and phrases: Fractional diffusion equations, drift, functional delay, numerical methods, order of convergence