Closed-form expressions for coefficients used in FD-TD high-order boundary conditions

Tirkas et al. recently presented an algorithm to implement absorbing boundary conditions (ABC's) of arbitrarily higher order into the finite difference-time domain technique. However, they did not provide explicit formulas to determine the expansion coefficients used in the Pade approximations of the pseudo-differential operator. Instead, the user is required to determine the roots of a polynomial using numerical methods that require computational effort and yield only approximate results. Exact expressions for the desired coefficients that are valid for Pade expansions of any order are presented.