Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel

  • Karczmarek P
  • Pylak D
  • Sheshko M
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Abstract

In this paper, exact solution of the characteristic equation with Cauchy kernel on the interval [-1, 1] is presented. Next, Jacobi polynomials are used to derive approximate solutions of the characteristic and general Cauchy-type singular integral equations. Moreover, estimations of errors of the approximated solutions are presented and proved. © 2006 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Approximate solutions
  • Cauchy kernel
  • Jacobi polynomials
  • Singular integral equations

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