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Direct variation method for solving hypersingular equations of diffraction

Keywords:

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


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.
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