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22 Dec 2016

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.

 

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