RESOLUTION OF CLASSICAL CAPACITY PROBLEMS BY MEANS OF A DIGITAL COMPUTER

Abstract

A completely general, yet easy to follow, numerical method is developed for estimating the capacity of an arbitrary surface S. The essence of the method is to first apply inversion to an associated exterior Dirichlet problem and then to estimate the solution at the origin of the resulting interior Dirichlet problem. This estimate is an approximation of the capacity of S and is obtained on a digital computer by a currently popular numerical technique. Estimates of capacities of cubes, ellipsoids, lenses, and toroids are obtained, and, whenever possible, comparisons are made with results obtained by other methods.