Displaying similar documents to “A new convergence rate for the quadrature method for solving singular integral equations”

On convergence of quadrature-differences method for linear singular integro-differential equations on the interval

A. I. Fedotov (2001)

Archivum Mathematicum

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Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval ( - 1 , 1 ) . We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.

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

Nikolaos I. Ioakimidis (1982)

Aplikace matematiky

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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...