Investigation on the stability of absorbing boundary conditions for the time-domain finite-difference method

Due to the instability of absorbing boundary conditions, numerical solutions spuriously grow as computations proceed; sooner or later, numerical errors override actual solutions. It has been found that the higher the order of the absorbing boundary condition applied, the stronger the instability. In the present work, it is shown that the instability originates from the computer roundoff error in the process of calculating boundary values. This error is further accumulated as the computation goes on. Numerical examples illustrate the instability caused by boundary conditions, and examine the way to suppress the instability.<>