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Further convergence results for two quadrature rules for Cauchy type principal value integrals

Nikolaos I. Ioakimidis — 1982

Aplikace matematiky

New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to 1 2 . The results obtained here supplement...

Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule

Nikolaos I. Ioakimidis;  Pericles S. Theocaris — 1978

Aplikace matematiky

The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval....

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