A comparison of transparent boundary conditions for the fresnel equation

We consider two numerical transparent boundary conditions that have been pr eviously introduced in the literature. The first condition (BPP) was propos ed by Baskakov and Popov (1991, Wave Motion 14. 121-128) and Papadakis et a l. (1992, J. Acoust. Soc. Am. 92, 2030-2038) while the second (SDY) is that of Schmidt and Deuflhard (1995, Comput, Math. Appl. 29, 53-76) and Schmidt and Yevick (1997, J. Comput. Phys. 134, 96-107). The latter procedure is e xplicitly tailored to the form of the underlying numerical propagation sche me and is therefore unconditionally stable and highly precise. Here we pres ent a new derivation of the SDY approach. As a result of this analysis, we obtain a simple modification of the BPP method that guarantees accuracy and stability for long propagation step lengths. (C) 2001 Academic Press.