International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 10957, 12 pages
doi:10.1155/2007/10957

Solution of Cauchy-type singular integral equations of the first kind with zeros of Jacobi polynomials as interpolation nodes

Abstract

Of concern in this paper is the numerical solution of Cauchy-type singular integral equations of the first kind at a discrete set of points. A quadrature rule based on Lagrangian interpolation, with the zeros of Jacobi polynomials as nodes, is developed to solve these equations. The problem is reduced to a system of linear algebraic equations. A theoretical convergence result for the approximation is provided. A few numerical results are given to illustrate and validate the power of the method developed. Our method is more accurate than some earlier methods developed to tackle this problem.