Runge-Kutta Methods for Integrating Differential Equations on High Speed Digital Computers

The Runge–Kutta methods of Gill, Strachey and Boulton are discussed in respect of their accuracy, speed and storage requirements on electronic digital computers. For machines possessing a double-length accumulator alternative integration procedures are suggested which are comparable in accuracy with Gill's process and which are likely to be considerably faster. These procedures use additional storage registers to carry guarding digits of the dependent variables where the methods of Gill and Strachey achieve their accuracy by subtle algebra.