Is there a numerical ODE solver facility in Maxima
Subject: Is there a numerical ODE solver facility in Maxima
From: Martin Schönecker
Date: Thu, 02 Apr 2009 20:13:45 +0200
(%i1) ? rk;
-- Function: rk (<ODE>, <var>, <initial>, <domain>)
-- Function: rk ([<ODE1>,...,<ODEm>], [<v1>,...,<vm>],
[<init1>,...,<initm>], <domain>)
The first form solves numerically one first-order ordinary
differential equation, and the second form solves a system of m of
those equations, using the 4th order Runge-Kutta method. <var>
represents the dependent variable. <ODE> must be an expression
that depends only on the independent and dependent variables and
defines the derivative of the dependent variable with respect to
the independent variable.
The independent variable is specified with `domain', which must be
a list of four elements as, for instance:
[t, 0, 10, 0.1]
the first element of the list identifies the independent variable,
the second and third elements are the initial and final values for
that variable, and the last element sets the increments that
should be used within that interval.
If <m> equations are going to be solved, there should be <m>
dependent variables <v1>, <v2>, ..., <vm>. The initial values for
those variables will be <init1>, <init2>, ..., <initm>. There
will still be just one independent variable defined by `domain',
as in the previous case. <ODE1>, ..., <ODEm> are the expressions
that define the derivatives of each dependent variable in terms of
the independent variable. The only variables that may appear in
those expressions are the independent variable and any of the
dependent variables. It is important to give the derivatives
<ODE1>, ..., <ODEm> in the list in exactly the same order used for
the dependent variables; for instance, the third element in the
list will be interpreted as the derivative of the third dependent
variable.
The program will try to integrate the equations from the initial
value of the independent variable until its last value, using
constant increments. If at some step one of the dependent
variables takes an absolute value too large, the integration will
be interrupted at that point. The result will be a list with as
many elements as the number of iterations made. Each element in
the results list is itself another list with <m>+1 elements: the
value of the independent variable, followed by the values of the
dependent variables corresponding to that point.
There are also some inexact matches for `rk'.
Try `?? rk' to see them.
(%o1) true
Best regards,
Martin