Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

A process for the step-by-step integration of differential equations in an automatic digital computing machine

S. Gilla1

a1 University Mathematical Laboratory Cambridge


It is advantageous in automatic computers to employ methods of integration which do not require preceding function values to be known. From a general theory given by Kutta, one such process is chosen giving fourth-order accuracy and requiring the minimum number of storage registers. It is developed into a form which gives the highest attainable accuracy and can be carried out by comparatively few instructions. The errors are studied and a simple example is given.

(Received June 03 1950)