A method of integrating Ordinary Differential Equations by using a trial step at
the midpoint of an interval to cancel out lower-order error terms. The second-order formula is

and the fourth-order formula is

(Press

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, pp. 896-897, 1972.

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press,
pp. 492-493, 1985.

Cartwright, J. H. E. and Piro, O. ``The Dynamics of Runge-Kutta Methods.'' *Int. J. Bifurcations Chaos* **2**, 427-449, 1992.
http://formentor.uib.es/~julyan/TeX/rkpaper/root/root.html.

Lambert, J. D. and Lambert, D. Ch. 5 in *Numerical Methods for Ordinary Differential Systems: The Initial Value Problem.* New York: Wiley, 1991.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Runge-Kutta Method'' and ``Adaptive
Step Size Control for Runge-Kutta.'' §16.1 and 16.2 in
*Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England:
Cambridge University Press, pp. 704-716, 1992.

© 1996-9

1999-05-25