Fourier series approximation for the Cauchy singular integral equation

Abstract

Using the Fourier series as a projection in the Galerkin method, we approach the solution of the Cauchy singular integral equation. This study is carried in \(L^2\). Numerical examples are developped to show the effectiveness of this method.

Keywords

• Singular integral equation
• Cauchy operator
• Galerkien method
• Fourier series