A supplement to the Runge-Kutta method

A SUPPLEMENT TO THE RUNGE-KUTTA METHOD* V. S. RESHETNIKOV 26 May 1970)

(Receiued

THE formulas presented below form a supplement to the Runge-Kutta method. It is well-known I1 j that the Runge-Kutta formulas for the system of differential equations i =

dyi/dx=fi(X,Yl,...,bn)r

1, 2, . . , n,

have the form

where hfz(xo, Y~o, I.. 3 Yno)t hfi(Xo f h / 2, Y~o + k3i = hf,(Xo + h / 2, Y~o + kti = kzi =

k&i =

hf,(xo

+ k, ylo + k31,

kii

/

kzi

/2,

2, . . * 1 Y~o $_

ktn

/2)-

. . . ( Yno

k2n

/2),

. . . , yno + hn).

It can be shown by the method described yi (50

+

(“/3kli

holds, where

0 <

t’~) = -

t <

Y io +

2f&,i

-

k,i’ 2/&,i

+

(-

+

+

‘/zk,i

in +

.2/2/3k4i) t3 +

k,i

Ill that the relation +

0 (Ii*)

k,i

-

‘/zkdi)

*’ $

t

1.

Translated by J. Berry REFERENCE 1.

*Zh.

BEREZIN, I. S. and ZHIDKOV, N. P. 2, Fizmatgiz, Moscow, 1962.

uj%hisl.

Mat. mat. Fiz.,

Computing

11, 3, 793, 1971.

329

Methods

(Metody vychislenii),

Vol.