#############################################################
# Building 'bvp1d4' and sample output on the SGIs
#############################################################
einstein% pwd; ls
/usr2/people/phy329/linsys/ex3

Makefile   bvp1d4.f
einstein% make
        f77 -g -n32 -c bvp1d4.f
        f77 -g -n32 -L/usr/localn32/lib -n32 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 -1.0547118733938987E-14
   6.2500000000000000E-02  0.3834724412118576    
   0.1250000000000000      0.7079302872941245    
   0.1875000000000000      0.9246563908935262    
   0.2500000000000000       1.000689732294703    
   0.3125000000000000      0.9244421766816860    
   0.3750000000000000      0.7075056502724236    
   0.4375000000000000      0.3828904610080090    
   0.5000000000000000     -3.1565329029368671E-15
   0.5625000000000000     -0.3828904610080154    
   0.6250000000000000     -0.7075056502724303    
   0.6875000000000000     -0.9244421766816929    
   0.7500000000000000      -1.000689732294711    
   0.8125000000000000     -0.9246563908935345    
   0.8750000000000000     -0.7079302872941338    
   0.9375000000000000     -0.3834724412118676    
    1.000000000000000     -2.4492935982947064E-16
 rmserr =   5.8394829778013078E-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 =   5.8394829778013078E-04
 rmserr =   2.5181486533000874E-05
 rmserr =   1.1531108217752065E-06
 rmserr =   5.8557438669720841E-08
 rmserr =   3.2465293440184777E-09
 rmserr =   1.8966747918271887E-10
 rmserr =   9.4215663095393918E-12

#############################################################
# Making output files for subsequent plotting via gnuplot.
# See previous handout for 'bvp1d' for typical 'gnuplot'
# "script" files.
#############################################################
einstein% bvp1d4 4 > out4
 rmserr =   5.8394829778013078E-04
einstein% bvp1d4 4 1 > err4
 rmserr =   5.8394829778013078E-04
einstein% bvp1d4 5 1 > err5
 rmserr =   2.5181486533000874E-05
einstein% bvp1d4 6 1 > err6
 rmserr =   1.1531108217752065E-06