International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 10957, 12 pages
Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes
Department of Mathematics, (Pure and Applied), University of Fort Hare, Alice 5700, South Africa
Received 16 February 2007; Revised 21 June 2007; Accepted 24 August 2007
Academic Editor: Michael John Evans
Copyright © 2007 G. E. Okecha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.