We consider the numerical solution of the time-fractional diffusion-wave equation on two-dimensional and three-dimensional unbounded spatial
domains. 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. Finite difference methods are used to solve the reduced problems on the
bounded computational domain and the stability of these finite difference methods are proved. The numerical results demonstrate that the method given in this paper is effective and feasible.