Opuscula Math. 28, no. 2 (2008), 179-194

Opuscula Mathematica

# Approximate solutions of a singular integral equation with Cauchy kernels in the quarter plane

Dorota Pylak

Abstract. In the paper, we present explicit formulae for the solution of the singular integral equation with Cauchy kernels in the quarter plane. Next, Jacobi and Chebyshev polynomials are used to derive approximate solutions of this equation.

Keywords: singular integral equation, Cauchy kernel, Chebyshev and Jacobi polynomials.

Mathematics Subject Classification: 65R20, 45L10, 45E05.

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