On polynomial collocation for second kind integral equations with fixed singularities of Mellin type (Q1402165)

The authors consider a method of polynomial collocation for the numerical solution of a second kind integral equation with an integral kernel of Mellin convolution type. Using a stability result by \textit{P. Junghanns} and \textit{A. Rathsfeld} [On polynomial collocation for Cauchy singular integral equations with fixed singularities. Integral Equations Operator Theory (to appear)], it is proved that the error of the approximate solution is less than a logarithmic factor times the best approximation and using the asymptotics of the solutions the rate of convergence is derived. Also an algorithm to compute the matrix stiffness is presented.