Numerical Examples

Abstract

Algorithms for calculating electrostatic fields, or linear functionals of these fields such as electrical capacitances, given in Chapters 2 and 3, are reduced to calculations of certain multiple integrals. From the point of view of numerical analysis one should integrate functions with at worst weak singularities. The numerical integration of such functions is a problem of independent interest. It has been discussed in detail for functions of one variable [38], but not much is known about multidimensional integrals of functions with weak singularities. The basic idea in the one-dimensional case is to integrate explicitly the singular part of the integrand and thus to reduce the problem to the integration of a smooth function. This problem is well understood.