Combinatorics-Based Recursive Closed Form Discrete Time Domain Green's Function for Soft and Hard boundaries

In this paper, combinatorial formulations are further developed using efficient recursive formulas, both for hard and soft boundary conditions. The resultant discrete Green's functions were verified by comparing them to numerical and frequency domain analytical results. Simulations of propagating pulses also show that the results produced directly over large distances indeed coincide with straightforward finite-difference time-domain (FDTD) calculations