Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain

We consider the numerical solution of the time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain. Introduce an artificial boundary and find the exact and approximate artificial boundary conditions for the given problem, which lead to a bounded computational domain. Using the exact or approximating boundary conditions on the artificial boundary, the original problem is reduced to an initial–boundary-value problem on the bounded computational domain which is respectively equivalent to or approximates the original problem. A finite difference method is used to solve the reduced problems on the bounded computational domain. The numerical results demonstrate that the method given in this paper is effective and feasible.