New methodologies for the calculation of Green´s functions for wave problems in two-dimensional unbounded domains

Authors

  • R. T. Couto Universidade Federal Fluminense

DOI:

https://doi.org/10.5540/tema.2013.014.01.0119

Abstract

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.

Author Biography

R. T. Couto, Universidade Federal Fluminense

Departamento de Matemática Aplicada

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.

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Published

2013-06-01

How to Cite

Couto, R. T. (2013). New methodologies for the calculation of Green´s functions for wave problems in two-dimensional unbounded domains. Trends in Computational and Applied Mathematics, 14(1), 119–130. https://doi.org/10.5540/tema.2013.014.01.0119

Issue

Vol. 14 No. 1 (2013)

Section

Original Article

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