Vladimir Pimenov, Ekaterina Tashirova
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