ode utility can produce a numerical solution to the
initial value problem for many systems of first-order ordinary
differential equations (ODE's).
ode can also be used to solve
systems of higher-order ODE's, since a simple procedure converts an
n'th-order equation into n first-order equations. The
ode can easily be piped to
graph, so that one or
more solution curves may be plotted as they are generated.
Three distinct schemes for numerical solution are implemented: Runge–Kutta–Fehlberg (the default), Adams–Moulton, and Euler. The Runge–Kutta–Fehlberg and Adams–Moulton schemes are available with adaptive stepsize.