A localized absorbing boundary condition for discretized parabolic equation

The exact DTBC derived is unconditionally stable and presents reflection-free boundary layer for PE problems. However, although is conditionally stable and not as accurate, the approximate DTBC is computationally more efficient thus applicable than the exact DTBC. The FD and narrow-angle PE constraints apply for both exact and approximate transfer functions, therefore the approximate transfer function would be preferable at farther ranges, that it reduces the convolution time significantly.