Ehrhardt, MatthiasMickens, Ronald E.2022-05-112022-05-112003-09-162197-8085https://depositonce.tu-berlin.de/handle/11303/16915http://dx.doi.org/10.14279/depositonce-15693In 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.en510 Mathematikdiscrete Airy equationdiscrete transparent boundary conditiondifference equationSchrödinger-type equationparabolic equation predictionResearch Paper