Condition of boundary integral equations in which the sought-for function and the given right-hand side are defined on different domains; round-off errors in the numerical solutions

摘要

Boundary integral equations in which the sought-for function and the given right-hand side are defined on different curves have the great advantage of regularity. Descretization of them, however, yields ill-conditioned systems of algebraic equations, i. e., systems susceptible to round-off errors. In this paper the round-off error is determined as a function of the number of nodes and as a function of the distance between the domains of definition of the solution and of the boundary values. The results corroborate and specify a theoretically deduced rule Heise (1978a) on how to carry out the numerical evaluation without spoiling the solution by round-off errors. An extensive survey of the paper is given in Sect. 2.