A Collocation Method for Cauchy Integral Equations in L2
In this paper we present a collocation method based on trigonometric polynomials combined with a regularization procedure, for solving Cauchy integral equations of the second kind, in L 2(0,2π). A system of linear equations is involved. We prove the existence of the solution for a double projection scheme, and we perform the error analysis. Some numerical examples illustrate the theoretical results.
KeywordsIntegral Equation Collocation Method Singular Integral Equation Trigonometric Polynomial Fredholm Integral Equation
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- [Mu53]Mushkelishvili, N.I.: Singular Integral Equations, Noordhoff, Groningen (1953). Google Scholar