The Determination of Axially Symmetric Fields by Digital Computation

Techniques have been developed to set uD field problems, governed by Laplace´s equation in finite-difference form, on a digital computer and solve them by iterative methods. The development of these techniques is outlined from a simple two-dimensional problem to more complicated three-dimensional axially symmetric problems. Methods are discussed that allow the simulation of open-field problems, the fitting of surfaces, and the particular case of Laplace´s equation along the axis of symmetry. These methods and techniques have been incorporated into special routines and functions to form the basis of a digital computer program that is now available for the solution of three-dimensional axially symmetric Laplacian field problems. This program is of a general nature that permits the solution to a range of problems with the minimum of effort required in the preparation of each particular one.