Journal of the Australian Mathematical Society

Research Article

Coefficients for the study of Runge-Kutta integration processes

J. C. Butchera1

a1 Department of Mathematics, University of Canterbury, Christchurch, New Zealand.

We consider a set of η first order simultaneous differential equations in the dependent variables y1, y2, …, yn and the independent variable x

S1446788700027932_eqn1

S1446788700027932_eqn1

S1446788700027932_eqn2

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
S1446788700027932_eqn3

(Received May 21 1962)