`ode`

ProgramThe GNU `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
output of `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.