Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes

Okecha, G. E.

doi:https://doi.org/10.1155/2007/10957

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 010957 | https://doi.org/10.1155/2007/10957

Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes

G. E. Okecha¹

Academic Editor: Michael John Evans

Received16 Feb 2007

Revised21 Jun 2007

Accepted24 Aug 2007

Published31 Oct 2007

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.

References

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Copyright

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.

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