Artificial Boundary Conditions Of Time-fractional Di Usion Equation And Time-fractional Schr?dinger Equation

We consider the numerical solution of the time-fractional di usion equation and time-fractional Schr?dinger equation on two-dimensional unbounded spatial domains.By introducing suitable artificial boundarys and finding the exact and approximate artificial boundary conditions for the given problems,which lead to bounded computational domains.For the time-fractional di usion equation,using the exact or approximating boundary conditions on the artificial boundary,the original problems are reduced to initial-boundaryvalue problems on the bounded computational domain which is respectively equivalent to or approximates the original problems.Finite di erence methods are used to solve the reduced problems on the bounded computational domains and the stability of these finite di erence methods are proved.