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<H2><A NAME="SECTION00513000000000000000"> </A><A NAME="1705"> </A><A NAME="1706"> </A>
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Initial Conditions and Default Ranges
</H2>
<P>
Initial conditions for the parameters and variables and their default
ranges may be declared using the INITIAL and RANGE commands. These specify
specific initial values for the parameters and variables and the default ranges
for display purposes. Any or all of the parameters and variables may
be specified in either case. We look at Duffing's equation, for example:
<P>
<PRE>
# The Duffing oscillator (duffing.def)
x' = y
y' = - alpha y + (beta - x^2) x + gamma cos(omega t)
t' = 1
INITIAL alpha 0.5 beta 0 gamma 10 omega 1
x -5 y 4 t 0
RANGE x -6 6 y -6 6
</PRE>
<P>
Note that in this example, we explicitly augment the phase space
with the variable t (else the parser will think t is a parameter).
When initial conditions or ranges are not specified, the default
values as given in Table <A HREF="node41.html#parser_defaults"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
SRC="/usr/lib/latex2html/icons.gif/cross_ref_motif.gif"></A> are used.
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<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
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