Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Direct variation method for solving hypersingular equations of diffraction


V.S. Eminova – Post-graduate Student, Novgorod State University Yaroslav the Wise. E-mail:

In the article, the integro-differential equation for problem of diffraction of H-polarization on a not closed perfectly conducting surface of revolution is studied. The hypersingular integro-differential equation is obtained. However, hypersingular operator has a more general form than in problems of diffraction on cylindrical surfaces. We have shown that hypersingular operator is positive definite, but inverse operator is completely continuous. As a result, the original integral-differential equation is equivalent to Fredholm’s equation of the second kind. We offered the direct variational method based on Chebyshev polynomials of the second kind, multiplied by the weight function for solutions of integro-differential equations. The basis functions satisfy certain conditions Meixner on the edge. It was solved an important problem of computing the matrix elements. It an example of calculation is considered and effectiveness of the proposed method is demonstrated.

  1. Vasil'ev E.N. Vozbuzhdenie tel vrashheniya. M.: Radio i svyaz'. 1987. 271 s.
  2. Zaxarov E.V., Pimenov Ju.V. Chislenny'j analiz difrakczii radiovoln. M.: Radio i svyaz'. 1982. 184 s.
  3. Sochilin A.V., E'minov I.S., E'minov S.I. Integro-differenczial'ny'e uravneniya linejny'x, bikonicheskix i krivolinejny'x vibratorny'x antenn // Antenny'. 2010. № 12. S. 27-34.
  4. E'minov S.I., Sochilin A.V. Chislenno-analiticheskij metod resheniya integral'ny'x uravnenij vibratorny'x antenn // Radiotexnika i e'lektronika. 2008. T. 53. № 5. S. 553-558.
  5. E'minov S.I. Teoriya integral'nogo uravneniya tonkogo vibratora // Radiotexnika i e'lektronika. 1993. T. 38. Vy'p. 12. S. 2160-2168.
  6. E'minov S.I. Analiticheskoe obrashhenie gipersingulyarnogo operatora i ego prilozheniya v teorii antenn // Pis'ma v ZhTF. 2004. T. 30. Vy'p. 22. S. 8-16.
  7. Mixlin S.G. Variaczionny'e metody' v matematicheskoj fizike. M.: Nauka. 1970. 420 s.
  8. Panasyuk V.V., Savruk M.P., Nazarchuk Z.T. Metod singulyarny'x integral'ny'x uravnenij v dvumerny'x zadachax difrakczii. Kiev: Naukova dumka. 1984. 344 s.

June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio