Numerical Solution of Ordinary and Partial Differential Equations by Means of Equivalent Circuits

Numerical methods are developed to solve certain types of linear and nonlinear partial differential equations to any desired degree of accuracy with the aid of equivalent electrical networks. The methods of solution of ordinary differential equations, both linear and nonlinear, follow as special cases. Three types of problems are considered:1. Initial‐value problems. If the field quantities are known along a surface, the networks may be solved by a straight‐forward step‐by‐step calculation. The networks may also be looked upon as supplying a ``schedule'' of operations that can be put on a digital calculating machine.For time‐varying problems new types of networks are developed in which time appears as an extra spatial variable. Examples of new networks for the elastic field and for the general nonlinear wave equation are given. Sample calculations and theoretical checks of a transient heat flow problem and of an ordinary differential equation are also included.2. Boundary‐value problems. Four methods of s...