Error analysis for absorbing boundary conditions (Q1109968)

An estimate is derived for the error committed by the introduction of artificial boundaries and corresponding artificial boundary conditions when solving wave equations on unbounded domains. The estimate has two terms. One is proportional to the largest reflection coefficient for the artificial boundary condition, the maximum taken only on those rays which appear in the computation. The second term is proportional to 1/k where k is a measure of the average frequency present in the solution.