Direct Method and Convergence Analysis for Some System of Singular Integro-Differential Equations

摘要

A class of singular integro-differential equations in Leheague spaces are studied. There are many applications of the singular integro- differential equations discussed in this paper. An example in modeling the stress distribution of an elastic medium with holes is discussed in the paper. Direct numerical schemes using a collocation method and a mechanical quadrature rule designed for the singular integro-differential equations are proposed for arbitrary smooth closed contours. Convergence analysis of theses methods are given. Numerical examples are also provided.