An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber
Bamberger, Alain ; Coron, François ; Ghidaglia, Jean-Michel
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 21 (1987), p. 405-424 / Harvested from Numdam
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Publié le : 1987-01-01
@article{M2AN_1987__21_3_405_0,
     author = {Bamberger, Alain and Coron, Fran\c cois and Ghidaglia, Jean-Michel},
     title = {An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {21},
     year = {1987},
     pages = {405-424},
     mrnumber = {908238},
     zbl = {0626.65136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1987__21_3_405_0}
}

Bamberger, Alain; Coron, François; Ghidaglia, Jean-Michel. An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 21 (1987) pp. 405-424. http://gdmltest.u-ga.fr/item/M2AN_1987__21_3_405_0/

[1] A. Bamberger, F. Coron and J. M. Ghidaglia, Analyse de la B.P.M.,méthode de résolution approchée de l'équation d'Helmholtz dans une fibreoptique, modélisation, convergence et stabilité. Rapport interne de l'ÉcolePolytechnique 151, Palaiseau, France, 1986.

[2] J. T. Beale and A. Majda, Rates of convergence for viscous splitting of the Navier-Stokes équations. Math. Comput. 37, 243-260 (1981). | MR 628693 | Zbl 0518.76027

[3] M. D. Feit and J. A. Fleck, Light propagation in graded-index optical fibers, AppL Opt. 17, 3990-3998 (1978).

[4] R. A. Fischer and W. K. Bischel, Numerical studies of the interplay betweenself phase modulation and dispersion for intense plane wave laser puises, J.Appl. Phys. 46, 4921-4934 (1975).

[5] A. Friedman, Partial differential équations, Holt Rinehart and Winston Inc., New York, 1969. | MR 445088 | Zbl 0224.35002

[6] J. L. Lions, Quelques méthodes de résolution desproblèmes aux limites nonlinéaires, Dunod, Paris, 1969. | Zbl 0189.40603

[7] J. L. Lions and E. Magenes, Nonhomogeneous boundary value problems andapplications, Springer, Berlin, 1972 (and Dunod, Paris 1968). | Zbl 0223.35039

[8] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. | MR 209834 | Zbl 0149.09501

[9] E. Stein and G. Weiss, Fourier analysis in euclidian spaces, Princeton, 1971.

[10] R. Temam, Sur la stabilité et la convergence de la méthode des pas fractionnaires, Ann. Math. Pura. AppL LXXIV, 1968, p.191-380. | MR 241838 | Zbl 0174.45804