New methodologies for the calculation of Green´s functions for wave problems in two-dimensional unbounded domains
DOI:
https://doi.org/10.5540/tema.2013.014.01.0119Abstract
This work describes the application of new methodologies for the evaluation of the inverse Fourier transforms that yield Green's functions for both the wave and Helmholtz equations in the entire bidimensional domain.References
G. Barton, "Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves", Oxford University Press, 1989.
E. Butkov, "Mathematical Physics", Addison-Wesley Publishing Company, Reading, Massachusetts, 1973.
R. Courant and D. Hilbert, "Methods of Mathematical Physics", Volume II, Third Printing, Interscience Publishers/John Wiley & Sons, New York, 1966.
B. Davies, "Integral Transforms and Their Applications", Texts in Applied Mathematics 41, Third Edition, Springer-Verlag, New York, 2002.
D. G. Duffy, "Green's Functions with Applications", Studies in Advanced Mathematics, Chapman & Hall/CRC Press LLC, Boca Raton, Florida, 2001.
E. N. Economou, "Green's Functions in Quantum Physics", Third Edition, Springer Series in Solid-State Sciences 7, Springer-Verlag, Berlin, 2006.
F. B. Hildebrand, "Advanced Calculus for Applications", Second Edition, Prentice-Hall, Englewood Cliffs, 1976.
H. P. Hsu, "Applied Fourier Analysis", HBJ Publishers, San Diego, 1984.
P. M. Morse and H. Feshbach, "Methods of Theoretical Physics", McGraw-Hill Book Company, New York, 1953.
R. Toscano Couto, Green's functions for the wave, Helmholtz and Poisson equations in a two-dimensional boundless domain, Rev. Bras. Ens. Fis., 35, No. 1 (2013), 1304.
G. N. Watson, "A Treatise on the Theory of Bessel Functions", Second Edition, Cambridge University Press, London, 1944.
Downloads
Additional Files
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.