Computer derivation of algebraic equations associated with runge-kutta formulas

The derivation of algebraic non-linear equations associated with Runge-Kutta formulas increases in complexity as the order of these formulas increases. To overcome this difficulty various operational methods have been devised. But these methods are quite involved and there also exists the possibility of human errors which may be difficult to detect. The aim of this paper is the derivation of these algebraic equations through a digital computer, the IBM 7094, using Fortran IV. The technique employed is based upon a mathematical method established by the first author. With the advent of the space age there arose a continuous need for Runge-Kutta formulas of higher and higher orders. It seems that the computer offers the best, if not the only, hope in keeping up with these needs.