On the approximate solution of some integral equations of the theory of elasticity and mathematical physics: PMM vol. 31, no. 6, 1967, pp. 1117–1131

Abstract

In this paper the development of the method presented in [1] is carried out with application to two types of integral equations encountered in mathematical physics in the investigation of many mixed problems with circular separation line of boundary conditions and in the investigation of plane mixed problems. The algorithm is given for reducing these integral equations to solution of equivalent infinite linear algebraic systems. It is proved that the resulting infinite systems are quasi completely regular for sufficiently large values of dimensionless parameter A which enters into the systems. It is shown that reduction (truncation) of infinite systems results in finite systems of linear algebraic equations with almost triangular matrices. The last circumstance simplifies considerably the solution of these finite systems after which the solution of initial integral equations is found from simple equations. For given accuracy of the approximate solution and decrease of parameter λ the number of equations in reduced systems increases. As an example the solution is presented for the axisymmetric problem of a die acting on an elastic layer lying without friction on a rigid foundation.