Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule

Abstract

The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval. An application of this method of numerical solution of singular integral equations is made in the case of a problem of the theory of plane elasticity.