Consider Bratu's equation
with boundary conditions 
, 
As in demo exp, a solution curve requires one free parameter;
here 
.
Note that additional parameters are specified in the user-supplied subroutine
PVLS in file pvls.f, namely,
(the 
-norm of 
),
(the minimum of 
on the space-interval [0,1] ),
(the boundary value 
).
These additional parameters should be considered as ``solution measures''
for output purposes; they should not be treated as true
continuation parameters.
Note also that four free parameters are specified in the AUTO-constants file
r.pvl.1, namely, , , , and .
The first one in this list, , is the true continuation parameter.
The parameters , , and are overspecified
so that their values will appear in the output.
However,
it is essential that the true continuation parameter appear first.
For example, it would be an error to specify the parameters
in the following order : , , , .
In general, true continuation parameters must appear first in the parameter-specification in the AUTO constants-file. Overspecified parameters will be printed, and can be defined in PVLS, but they are not part of the intrinsic continuation procedure.
As this demo also illustrates (see the UZR values in r.pvl.1), labeled solutions can also be output at selected values of the overspecified parameters.
| COMMAND | ACTION |
| mkdir pvl | create an empty work directory |
| cd pvl | change directory |
| @dm pvl | copy the demo files to the work directory |
| cp r.pvl.1 r.pvl | get the constants-file |
| @r pvl | compute a solution branch |
| @sv pvl | save output-files as p.pvl, q.pvl, d.pvl |