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The Plotutils Package

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.

8.1 Mathematical basics		Ordinary differential equations
8.2 Simple examples using ode		Simple examples using ode
8.3 Additional examples using ode		Additional examples using ode
8.4 ode command-line options		ode command-line options
8.5 Diagnostic messages
8.6 Numerical error and how to avoid it
8.7 Running time		Time spent running ode
8.8 The ode input language formally specified		The ode input language formally specified
8.9 Bibliography on ode and solving differential equations		Bibliography on ode and ODE's