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A novel numerical technique to investigate nonlinear guided waves: Approximation of nonlinear Schrödinger equation by nonperiodic pseudospectral methods
Author(s) -
De Veronico C.,
Funaro D.,
Reali G. C.
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100603
Subject(s) - mathematics , classification of discontinuities , nonlinear system , gauss pseudospectral method , mathematical analysis , trigonometry , planar , nonlinear schrödinger equation , trigonometric functions , boundary value problem , algebraic number , pseudo spectral method , algebraic equation , schrödinger equation , geometry , physics , fourier transform , quantum mechanics , fourier analysis , computer graphics (images) , computer science
A new numerical technique for investigating light waves guided by planar nonlinear dielectric films is presented. The method implements a multidomain spectral type approximation based on orthogonal algebraic polynomials, and makes possible to deal with nonperiodic boundary conditions and discontinuities of the data, overcoming the known deficiencies of the trigonometric polynomials. Results of preliminary numerical experiments for the solution of the nonlinear Schrödinger equation are presented. © 1994 John Wiley & Sons, Inc.