Numerical solution for systems of second-ordered singular integral equations and their physics representation

摘要

The present work deals with the numerical solution for a system of second-ordered singular integral equations of the first kind. The analytical solution of hypersingular operator is obtained and used to develop an efficient approximate solution. Relating the Hadamard integrals to Cauchy principal-value integrals, we expand the singular kernel and the density function of hypersingular integral equation based first and second kinds Chebyshev series of order N. Furthermore, the analytical findings are applied successfully for the mathematical model of antenna work problem where the kernel function has a discontinuity at the feeding points. A numerical example are given to demonstrate the performance of the present schemes.