Discrete Variational Green's Function. II. One Dimensional Problem.
A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.
Non-linear singular integral equations are investigated in connection with some basic applications in two-dimensional fluid mechanics. A general existence and uniqueness analysis is proposed for non-linear singular integral equations defined on a Banach space. Therefore, the non-linear equations are defined over a finite set of contours and the existence of solutions is investigated for two different kinds of equations, the first and the second kind. Moreover, the existence of solutions is further...