Open AccessOn the approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam
Author(s) -
Lewis F. Richardson
Publication year - 1910
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1910.0020
Subject(s) - arithmetic function , mathematics , boundary (topology) , simple (philosophy) , class (philosophy) , boundary value problem , differential equation , relation (database) , mathematical analysis , algebra over a field , pure mathematics , computer science , philosophy , epistemology , artificial intelligence , database
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.