Geodesic
Integration of oscillating functions in a quasi-three-dimensional electrodynamic problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 301-312 
I. V. Oseledets; S. L. Stavtsev; E. E. Tyrtyshnikov. Integration of oscillating functions in a quasi-three-dimensional electrodynamic problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 301-312. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a8/
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     title = {Integration of oscillating functions in a~quasi-three-dimensional electrodynamic problem},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Numerical methods designed for the integration of oscillating functions are compared. The methods are applied to a quasi-three-dimensional electrodynamic problem.

[1] Tyrtyshnikov E. E., “Structured preconditioned for operator equations”, Numer. Linear Algebra Appl., 12 (2002), 251–259 | DOI | MR

[2] Dmitriev V. I., Zakharov E. B., Integralnye uravneniya v kraevykh zadachakh elektrodinamiki, Izd-vo MGU, M., 1987 | MR

[3] Tyrtyshnikov E. E., “Modifikatsii metodov vychisleniya integralov Chebyshëva–Lagerra i Gaussa–Lezhandra”, Zh. vychisl. matem. i matem. fiz., 44:7 (2004), 1187–1195 | MR | Zbl

[4] Smelov V. V., “O kvadraturakh tipa Gaussa, osnovannykh na trigonometricheskikh bazisakh”, Matem. modelirovanie, 20:3 (2008), 302–308 | MR

[5] Mori M., “Discovery of the double exponential transformation and its developments”, Res. Inst. Math. Sei. Kyoto Univ., 41 (2005), 897–935 | DOI | MR | Zbl

[6] Stenger F., “Intergation formulas based on the trapezoidal formula”, J. Appl. Math., 12 (1973), 103–114 | MR | Zbl

[7] Takuya Ooura, Masatake Mori, “A robust double exponential formula for Fourier-type integrals”, J. Comput. and Appl. Math., 112 (1999), 299–241 | MR

[8] Krylov V. I., Priblizhennoe vychislenie integralov, Fizmatgiz, M., 1959 | MR

[9] Geronimus Ya. L., Teoriya ortogonalnykh mnogochlenov, Gostekhteorizdat, L., 1950