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.