8 The ode Program

The 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.

• Basic Math: Ordinary differential equations
• Simple ode Examples: Simple examples using ode
• Additional ode Examples: Additional examples using ode
• ode Invocation: ode command-line options
• Diagnostics: Diagnostic messages
• Numerical Error: Numerical error and how to avoid it
• Running Time: Time spent running ode
• Input Language: The ode input language formally specified
• ODE Bibliography: Bibliography on ode and ODE's