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

作者：Simon P.A. Gill · 发表于：Mathematical Proceedings of the Cambridge Philosophical Society · 年份：1951 · DOI：10.1017/s0305004100026414 · 被引用次数：445 · 研究领域：Numerical methods for differential equations、Numerical Methods and Algorithms、Modeling and Simulation Systems

Abstract 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.