Improving Round-off in Runge-Kutta Computations with Gill's Method

Abstract

Runge-Kutta-Gill scheme in common use is based on an incomplete adaptation for floating point operations of Gill's method. An improved version reduces round-ofF error significantly. In this note the heart of the scheme is presented in Fortran language. It is then shown how an improved version of the method can be obtained with the addition of two Fortran statements. The two versions are algebraically equivalent, but computationally the new version is a significant improvement. A numerical example comparing the two is included. © 1970, ACM. All rights reserved.