Article,
The Resistive Net and Finite-Difference Equations
American Journal of Physics, 40 (9): 1246--1257 (1972)
DOI: 10.1119/1.1986809
Abstract
The application of finite-differenceequations in the solution of repetitive multiloop resistive circuits in one-and two-dimensional configurations is discussed in both finite and infinite cases. The technique of solution involves only ordinary algebra and trigonometry. Yet one can see the emergence of simple orthogonal functions and the finite-difference approximations of the Cauchy-Riemann equations and Laplace's equation.Boundary-value problems can be presented and understood at a simple level of physics and mathematics. Such repetitive structures can serve as discrete approximative models for various physical properties of continuous media. The implications for the teaching of boundary-value problems in electricity are brought out.
