On polynomial collocation for second kind integral equations with fixed singularities of Mellin type
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.
integral kernel of Mellin convolution type stability
scientific article; zbMATH DE number 1967704