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

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  • G. E. Okecha

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.

Suggested Citation

  • G. E. Okecha, 2007. "Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-12, October.
    • Handle: RePEc:hin:jijmms:010957
    DOI: 10.1155/2007/10957
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