A Simple Procedure for Improved Accuracy in the Resistor-Network Solution of Laplace’s and Poisson’s Equation

The necessity for practical solutions of Laplace’s and Poisson’s equations arises frequently in engineering; for example, in problems of steady-state temperature, electric and gravitational potential, incompressible fluid flow, elastic torsion, and other problems of elasticity. It is well known that these equations can be solved by resistor networks (1). In this note it is shown that in solving the equation where by a resistor network, it is possible to reduce greatly the lumping or truncation error by simply adding additional resistors to the usual arrangement, without any increase in the number of mesh points.