The numerical solution of Singular Integral Equations of Cauchy-type at a discrete set of points t1is obtained through discretization of the original equation with the Gauss-Jacobi quadrature. The natural or Nyström'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 C1 functions. Finally, error bounds are derived, and for C functions it is shown that Nyström's formula converges faster than Lagrange's interpolation polynomials.
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics
- Singular integral equations Nyströ
- s interpolation convergence