Abstract
The numerical solution of Singular Integral Equations of Cauchy-type at a discrete set of points ti is obtained through discretization of the original equation with the Gauss-Jacobi quadrature. The natural or Nystrom's interpolation formula is used to approximate the solution of the equation for points different from ti. Uniform convergence of the interpolation formula is shown for C 1 functions. Finally, error bounds are derived, and for C∞ functions it is shown that Nystrom's formula converges faster than Lagrange's interpolation polynomials.
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