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On one approach to finding the branching lines and bifurcation points of solutions of nonlinear integral equations whose kernels depend analytically on two spectral parameters

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We consider iterative algorithms of finding the curves of eigenvalues and their bifurcation points of a nonlinear algebraic two-parameter spectral problem, which appears in the solution of the problem of synthesis of plane antenna arrays by a given amplitude directivity pattern. These algorithms are based on the numerical procedure of calculation of ordinary and partial derivatives of a matrix determinant and the algorithm of finding all eigenvalues in a given domain of change in the spectral parameters. We also present some results of numerical experiments.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    B. M. Podlevs’kyi

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  1. B. M. Podlevs’kyi
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 3, pp. 15–29, July–September, 2009.

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Podlevs’kyi, B.M. On one approach to finding the branching lines and bifurcation points of solutions of nonlinear integral equations whose kernels depend analytically on two spectral parameters. J Math Sci 171, 433–452 (2010). https://doi.org/10.1007/s10958-010-0148-y

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  • DOI: https://doi.org/10.1007/s10958-010-0148-y

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