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

Apostolos Gerasoulist

doi:10.1080/00207168408803407

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

Apostolos Gerasoulist

School of Arts and Sciences, Computer Science

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	143-161
Number of pages	19
Journal	International Journal of Computer Mathematics
Volume	15
Issue number	1-4
DOIs	https://doi.org/10.1080/00207168408803407
State	Published - 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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10.1080/00207168408803407

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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 Nystr{\"o}m'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 Nystr{\"o}m's formula converges faster than Lagrange's interpolation polynomials.",

keywords = "Singular integral equations Nystr{\"o}, m's, s interpolation convergence",

author = "Apostolos Gerasoulist",

note = "Funding Information: ?This research has been partially supported by a grant and a summer Fellowship from the Rutgers Research Council.",

year = "1984",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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