Numerical Solution of Singular Integral Equations: Applications

A large variety of boundary-type problems of mathematical physics are investigated, with the results of the investigation summarized; a table is provided as a user manual to engineers familiar in solving boundary-value problems with the aid of the integral equations technique. The methods for the numerical solution of one-dimensional singular integral equations developed previously by a large number of investigators are exact for integrands which are polynomials of degree up to 2n-1 and not n-1, as it was believed. In general, the Lobatto-type methods of numerical solution of Cauchy-type singular integral equations are shown to be very convenient for the calculations arising in plane elasticity problems. The Gauss-, Radau- and Lobatto-type numerical integration rules are, in general, the best rules to be used for the numerical solution of Cauchy-type singular integral equations.