AbstractThe numerical solution of Singular Integral Equations of Cauchytype at a discrete set of point's 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 than ti. Uniform convergence of the interpolation formula is shown for C1 functions. Finally, error bounds are derived and for smooth function it is shown that Nystrom's formula converges faster than Lagrange's interpolation polynomials.
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