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Mathematical models based on singular integral equations with non-Carleman shift. Analysis of solvability and numerical methods of solution

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We consider some examples of systems whose functionality can be described with the help of mathematical models based on singular integral equations with non-Carleman shift. For this type of equations, we have obtained an estimate for the dimension of the kernel of the corresponding operator and proposed numerical methods for both evaluating the dimension of the kernel and constructing solutions.

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Authors and Affiliations

  1. Department of Hydroacoustics, Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Odessa, Ukraine

    A. A. Batyrev

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  1. A. A. Batyrev
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 2, pp. 50–54, April–June, 2009.

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Batyrev, A.A. Mathematical models based on singular integral equations with non-Carleman shift. Analysis of solvability and numerical methods of solution. J Math Sci 170, 622–628 (2010). https://doi.org/10.1007/s10958-010-0107-7

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  • DOI: https://doi.org/10.1007/s10958-010-0107-7

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