Stability and convergence limitations on the use of analogue computers with resistance network analogues

Abstract

Various practical methods have been described for solving partial differential equations such as ∇2 = f() by means of resistance networks coupled to electronic analogue computing units. These schemes are investigated mathematically to determine the conditions for which the computer remains stable, or for which the successive approximations converge to the required solution. It is shown that all the methods will break down if the gradient df/d is negative and sufficiently large to cause the correct solution to be wave-like.