Preprint 29-2003

Solutions to the Discrete Airy Equation: Application to Parabolic Equation Calculations

Author(s) : Matthias Ehrhardt , Ronald E. Mickens

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 29-2003

PACS : 02.70.Bf, 43.30+m, 92.10.Vz

Abstract :
n the case of the equidistant discretization of the Airy differential equation (``discrete Airy equation'') the exact solution can be found explicitly. This fact is used to derive a discrete transparent boundary condition (TBC) for a Schrödinger-type equation with linear varying potential, which can be used in ``parabolic equation'' simulations in (underwater) acoustics and for radar propagation in the troposphere. We propose different strategies for the discrete TBC and show an efficient implementation. Finally a stability proof for the resulting scheme is given. A numerical example in the application to underwater acoustics shows the superiority of the new discrete TBC.

Keywords : discrete Airy equation, discrete transparent boundary condition, difference equation, Schrödinger-type equation, parabolic equation prediction

Notes :
submitted to: Journal of Computational and Applied Mathematics.