Solutions to the Discrete Airy Equation: Application to Parabolic Equation Calculations
| dc.contributor.author | Ehrhardt, Matthias | |
| dc.contributor.author | Mickens, Ronald E. | |
| dc.date.accessioned | 2022-05-11T12:11:51Z | |
| dc.date.available | 2022-05-11T12:11:51Z | |
| dc.date.issued | 2003-09-16 | |
| dc.description.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. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/16915 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-15693 | |
| dc.language.iso | en | |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | discrete Airy equation | en |
| dc.subject.other | discrete transparent boundary condition | en |
| dc.subject.other | difference equation | en |
| dc.subject.other | Schrödinger-type equation | en |
| dc.subject.other | parabolic equation prediction | en |
| dc.title | Solutions to the Discrete Airy Equation: Application to Parabolic Equation Calculations | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2003, 29 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |