A modified discrete spectral collocation method for first kind integral equations with logarithmic kernel
The author considers Symm's integral equation, i.e. a first kind integral equation with logarithmic kernel. He proposes a modification of the discrete Galerkin method presented by \textit{K. E. Atkinson} [ibid. 1, No. 3, 343-363 (1988; Zbl 0676.65140)]. This method has the computational complexity of the trigonometric collocation but it still retains the stability and the convergence properties of the original trigonometric Galerkin method. The given theory is illustrated by numerical experiments.
first kind integral equation with logarithmic kernel
scientific article; zbMATH DE number 575548
scientific article