#############################################################
# Building 'bvp1d' and sample output on the SGIs
#############################################################

einstein% pwd; ls
/usr2/people/phy329/linsys/ex3
Makefile   bvp1d4.f

einstein% make
   f77 -g -c bvp1d4.f
   f77 -g -L/usr/local/lib bvp1d4.o \
       -lp329f -llapack -lblas -o bvp1d4

einstein% bvp1d4
 usage: bvp1d4 <level> [<option>]

        Specify option .ne. 0 for output
        of error instead of solution

#############################################################
# Note: compare with completely second-order 'bvp1d 4'
# which results in rms error of approximately 9.0E-03.
# These results are about 15 times better at this resolution
# (h = 1/16).
#############################################################
einstein%  bvp1d4 4
   0.0000000000000000E+00 -2.1094237467877974E-15
   6.2500000000000000E-02  0.3834724412118644    
   0.1250000000000000      0.7079302872941298    
   0.1875000000000000      0.9246563908935299    
   0.2500000000000000       1.000689732294706    
   0.3125000000000000      0.9244421766816876    
   0.3750000000000000      0.7075056502724246    
   0.4375000000000000      0.3828904610080095    
   0.5000000000000000     -3.1565329029368671E-15
   0.5625000000000000     -0.3828904610080158    
   0.6250000000000000     -0.7075056502724310    
   0.6875000000000000     -0.9244421766816937    
   0.7500000000000000      -1.000689732294711    
   0.8125000000000000     -0.9246563908935347    
   0.8750000000000000     -0.7079302872941337    
   0.9375000000000000     -0.3834724412118674    
    1.000000000000000      0.0000000000000000E+00
 rmserr =   5.8394829778185022E-04

#############################################################
# Convergence test: Solve BVP on a sequence of levels,
# redirect stdout so that only overall RMS error appears 
# on terminal.  Rate of convergence is not as definitive 
# as it was for the second order calculation, but clearly 
# this method converges much more rapidly than the second
# order method.
#############################################################
einstein% foreach level (4 5 6 7 8 9 10)
foreach? bvp1d4 $level > /dev/null
foreach? end
 rmserr =   5.8394829778185022E-04
 rmserr =   2.5181486528917311E-05
 rmserr =   1.1531108254396499E-06
 rmserr =   5.8557458836146244E-08
 rmserr =   3.2464482687331829E-09
 rmserr =   1.8917403769211032E-10
 rmserr =   9.3084206800586618E-12

#############################################################
# Making output files for subsequent plotting via gnuplot.
# See Class Notes for postscript and previous days notes 
# for typical 'gnuplot' script files.
#############################################################
einstein% bvp1d4 4 > out4
 rmserr =   5.8394829778185022E-04

einstein% bvp1d4 4 1 > err4
 rmserr =   5.8394829778185022E-04

einstein% bvp1d4 5 1 > err5
 rmserr =   2.5181486528917311E-05

einstein% bvp1d4 6 1 > err6
 rmserr =   1.1531108254396499E-06