Timing
This demo can be used to gain insight into the computer time
needed as a function of the dimension NDIM and the number of
mesh intervals NTST. The test problem is a system of boundary
value problems (BVP) written in first order form. The system's
dimension can be any even number. The BVP consists of (NDIM/2)
identical copies of the Gelfand-Bratu BVP (see the AUTO demo
"Gelfand-Bratu/Original"). To increase the complexity of the
equations somewhat, the exponential function in the Gelfand-
Bratu equation is explicitly computed by a Taylor polynomial
with a relatively large number of terms, as programmed in the
equations-file tim.f90. The number of Gauss collocation points
used in each mesh interval is set at the customary recommended
value NCOL=4.
To run this demo type "auto tim.auto". As currently set in the
python script "tim.auto", the timing run will be done for the
following three selections of NDIM and NTST:
(NDIM,NTST) = (10,50) , (10,100) , (10,200)
where each of these three runs does 182 continuation steps.
The output files b.ndim10-ntst50, s.ndim10-ntst50, etc., can
be plotted using the shell commands "@pp ndim10-ntst50" and
"@pl ndim10-ntst50". The number of iterations for each step can
be seen by typing "@it ndim10-ntst50" in the shell window.
If one makes changes in the values of NDIM or NTST or other
AUTO-constants such as NCOL, then one should check that each
run takes the same number of continuation steps and also that
the number of Newton iterations is the same, in order for the
timing comparison to be fair.