Singular Integral Equations—The Convergence of the Gauss-Jacobi Quadrature Method

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)143-161
Number of pages19
JournalInternational Journal of Computer Mathematics
Volume15
Issue number1-4
DOIs
StatePublished - Jan 1984

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

Keywords

  • Singular integral equations Nyströ
  • m's
  • s interpolation convergence

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