%0 Journal Article
%T Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes
%A G. E. Okecha
%J International Journal of Mathematics and Mathematical Sciences
%D 2007
%I Hindawi Publishing Corporation
%R 10.1155/2007/10957
%X 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.
%U http://www.hindawi.com/journals/ijmms/2007/010957/abs/