Coefficients for the study of Runge-Kutta integration processes

Abstract

We consider a set of η first order simultaneous differential equations in the dependent variables y1, y2, …, yn and the independent variable x ⋮ No loss of gernerality results from taking the functions f1, f2, …, fn to be independent of x, for if this were not so an additional dependent variable yn+1, anc be introduced which always equals x and thus satisfies the differential equation