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On a System of p ‐Tuple Series Equations Related to the Scattering by an Inhomogeneous Sphere
Author(s) -
Idemen Mithat
Publication year - 1978
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19780580406
Subject(s) - series (stratigraphy) , mathematics , uniqueness , algebraic equation , mathematical analysis , simultaneous equations , system of linear equations , scattering , convergence (economics) , neumann series , legendre polynomials , differential equation , nonlinear system , physics , paleontology , quantum mechanics , economic growth , optics , economics , biology
A system of p‐tuple series equations, involving associate Legendre functions, related to the scattering of electromagnetic waves by a spherical surface divided into p parallel strips with different impedances is studied. The original problem of solving a system composed of two p‐tuple series equations is reduced to a problem of solving 2(2p—1) (or two) completely independent p‐tuple series equations with the same kernel as well as a system of linear algebraic equations. The solutions to the independent series equations can be found by successive iterations. The conditions wich guarantee the convergence of the iterations and the uniqueness of the solution are given in two theorems. The results are applied to a simple illustrative example.