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Calculation of special functions arising in the problem of diffraction by a dielectric ballстатья
Статья опубликована в журнале из списка Web of Science и/или Scopus
- Автор: Malyshev K.Yu
- Журнал: Discrete and Continuous Models and Applied Computational Science
- Том: 29
- Номер: 2
- Год издания: 2021
- Издательство: Изд-во РУДН
- Местоположение издательства: М.
- Первая страница: 146
- Последняя страница: 157
- DOI: 10.22363/2658-4670-2021-29-2-146-157
- Аннотация: To apply the incomplete Galerkin method to the problem of the scattering of electromagnetic waves by lenses, it is necessary to study the differential equations for the field amplitudes. These equations belong to the class of linear ordinary differential equations with Fuchsian singularities and, in the case of the Lüneburg lens, are integrated in special functions of mathematical physics, namely, the Whittaker and Heun functions.The Maple computer algebra system has tools for working with Whittaker and Heun functions, but in some cases this system gives very large values for these functions,and their plots contain various kinds of artifacts. Therefore, the results of calculationsin the Maple’11 and Maple’2019 systems of special functions related to the problemof scattering by a Lüneburg lens need additional verification. For this purpose, an algorithm for finding solutions to linear ordinary differential equations with Fuchsian singular points by the method of Frobenius series was implemented, designed asa software package Fucsh for Sage. The problem of scattering by a Lüneburg lensis used as a test case. The calculation results are compared with similar resultsobtained in different versions of CAS Maple.Fuchs for Sage allows computing solutions to other linear differential equationsthat cannot be expressed in terms of known special functions.
- Добавил в систему: Малышев Ксаверий Юрьевич