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Main Title: Solutions to the Discrete Airy Equation: Application to Parabolic Equation Calculations
Author(s): Ehrhardt, Matthias
Mickens, Ronald E.
Type: Research Paper
Abstract: In 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.
Subject(s): discrete Airy equation
discrete transparent boundary condition
difference equation
Schrödinger-type equation
parabolic equation prediction
Issue Date: 16-Sep-2003
Date Available: 11-May-2022
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 29
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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