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Error estimates for external approximation of ordinary differential equations and the superconvergence property

Teresa Regińska (1988)

Aplikace matematiky

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.

Existence and uniqueness for non-linear singular integral equations used in fluid mechanics

E. G. Ladopoulos, V. A. Zisis (1997)

Applications of Mathematics

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...

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