A note on the convergence of product integration and Galerkin method for weakly singular integral equations
The paper deals with weakly singular Fredholm type integral equations, where the kernels and their derivatives satisfy algebraic conditions studied by \textit{G. Vainikko} and \textit{A. Pedas} [J. Aust. Math. Soc., Ser. B. 22, 419-430 (1981; Zbl 0475.65085)]. The author obtains the optimal convergence of product integration and Galerkin methods using piecewise polynomials on suitably graded meshes. For proper quadrature rules and iterated Galerkin solutions superconvergence results are obtained.
weakly singular Fredholm type integral equations
product integration and Galerkin methods
scientific article; zbMATH DE number 1088840
scientific article