On the Solvability of Singular Integral Equations Via Gauss-Jacobi Quadrature

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Abstract

A direct method of solving Cauchy type singular integral Eqs. of second kind with “constant coefficients” based on the Gauss-Jacobi quadrature and collocation at the zeros of Jacobi polynomials is studied. For the dominant Eq. it is shown that the coefficient matrix of the resulting linear algebraic system has a neat closed form expression, and that the magnitude of its determinant is unformly bounded below away from zero. It is further shown that the linear algebraic system obtained from the complete singular integral Eq. using the direct method is equivalent to the system of Eqs. derived from the regularized Fredholm integral Eq. of the second kind using appropriate Gaussian quadrature. From this equivalence follow the existence and uniqueness of the solution of the linear algebraic system corresponding to the complete Eq.

Original languageEnglish (US)
Pages (from-to)59-75
Number of pages17
JournalInternational Journal of Computer Mathematics
Volume12
Issue number1
DOIs
StatePublished - Jan 1 1982

All Science Journal Classification (ASJC) codes

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

Keywords

  • Cauchy type
  • Existence
  • Gauss-Jacobi Quadrature
  • Singular Integral Equations
  • Uniqueness

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