On the approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam

Abstract

In order to deal with irregular boundaries, analysis is replaced by arithmetic, continuous functions are represented by tables of numbers, differentials by central differences. Problems then fall into two classes:— (A) The relation between the equation obtaining throughout the body, and the boundary condition is such that the integral can be stepped out from a boundary. This class includes equations of all orders and degrees. It has been treated by arithmetical differences by Runge, W. F. Sheppard, Karl Heun, W. Kutta, and Richard Ganz. Examples of a specially simple method are given.