c example of a stiff diff eq. d^2y/dt^2+1001dy/dt+1000y=0.
yex(t) =(1./999.)*(1001.*exp(-t)-exp(-1000.*t) )
t1=1./1001.
t2=1./sqrt(1.E3)
tscale1=amin1(t1,t2)
dt=tscale1/5.
tf=3.
nstep=int(tf/dt)
kp=int(float(nstep)/60.)
kount=kp
y0=1.
y1=1.
print*,'t1,t2,dt=',t1,t2,dt
print*,' '
print 100,0., y0 ,yex(0.)
do 10 i=2,nstep
t=dt*float(i)
y2=2.*y1-y0+( -1001.*(y1-y0)*dt -dt**2*1000.*y1)
if(i.eq.kount) then
print 100,t, y2 ,yex(t)
kount=kount+kp
endif
y0=y1
y1=y2
10 continue
100 format( 1x,'t,y,yex=',3(4x,e11.4))
stop
end
t1,t2,dt= 0.000999000971 0.0316227786 0.000199800197
t,y,yex= 0.0000E+00 0.1000E+01 0.1001E+01
t,y,yex= 0.4995E-01 0.9522E+00 0.9532E+00
t,y,yex= 0.9990E-01 0.9059E+00 0.9067E+00
t,y,yex= 0.1499E+00 0.8617E+00 0.8626E+00
t,y,yex= 0.1998E+00 0.8198E+00 0.8205E+00
t,y,yex= 0.2498E+00 0.7798E+00 0.7806E+00
t,y,yex= 0.2997E+00 0.7418E+00 0.7425E+00
t,y,yex= 0.3497E+00 0.7057E+00 0.7063E+00
t,y,yex= 0.3996E+00 0.6713E+00 0.6719E+00
t,y,yex= 0.4496E+00 0.6386E+00 0.6392E+00
t,y,yex= 0.4995E+00 0.6075E+00 0.6080E+00
t,y,yex= 0.5495E+00 0.5779E+00 0.5784E+00
t,y,yex= 0.5994E+00 0.5497E+00 0.5502E+00
t,y,yex= 0.6494E+00 0.5229E+00 0.5234E+00
t,y,yex= 0.6993E+00 0.4974E+00 0.4979E+00
t,y,yex= 0.7493E+00 0.4732E+00 0.4737E+00
t,y,yex= 0.7992E+00 0.4502E+00 0.4506E+00
t,y,yex= 0.8492E+00 0.4282E+00 0.4286E+00
t,y,yex= 0.8991E+00 0.4074E+00 0.4078E+00
t,y,yex= 0.9491E+00 0.3875E+00 0.3879E+00
t,y,yex= 0.9990E+00 0.3686E+00 0.3690E+00
t,y,yex= 0.1049E+01 0.3507E+00 0.3510E+00
t,y,yex= 0.1099E+01 0.3336E+00 0.3339E+00
t,y,yex= 0.1149E+01 0.3173E+00 0.3176E+00
t,y,yex= 0.1199E+01 0.3019E+00 0.3022E+00
t,y,yex= 0.1249E+01 0.2872E+00 0.2874E+00
t,y,yex= 0.1299E+01 0.2732E+00 0.2734E+00
t,y,yex= 0.1349E+01 0.2599E+00 0.2601E+00
t,y,yex= 0.1399E+01 0.2472E+00 0.2474E+00
t,y,yex= 0.1449E+01 0.2352E+00 0.2354E+00
t,y,yex= 0.1499E+01 0.2237E+00 0.2239E+00
t,y,yex= 0.1548E+01 0.2128E+00 0.2130E+00
t,y,yex= 0.1598E+01 0.2024E+00 0.2026E+00
t,y,yex= 0.1648E+01 0.1926E+00 0.1928E+00
t,y,yex= 0.1698E+01 0.1832E+00 0.1834E+00
t,y,yex= 0.1748E+01 0.1743E+00 0.1744E+00
t,y,yex= 0.1798E+01 0.1658E+00 0.1659E+00
t,y,yex= 0.1848E+01 0.1577E+00 0.1578E+00
t,y,yex= 0.1898E+01 0.1500E+00 0.1502E+00
t,y,yex= 0.1948E+01 0.1427E+00 0.1428E+00
t,y,yex= 0.1998E+01 0.1358E+00 0.1359E+00
t,y,yex= 0.2048E+01 0.1291E+00 0.1293E+00
t,y,yex= 0.2098E+01 0.1228E+00 0.1230E+00
t,y,yex= 0.2148E+01 0.1169E+00 0.1170E+00
t,y,yex= 0.2198E+01 0.1112E+00 0.1113E+00
t,y,yex= 0.2248E+01 0.1058E+00 0.1058E+00
t,y,yex= 0.2298E+01 0.1006E+00 0.1007E+00
t,y,yex= 0.2348E+01 0.9570E-01 0.9578E-01
t,y,yex= 0.2398E+01 0.9104E-01 0.9112E-01
t,y,yex= 0.2448E+01 0.8660E-01 0.8668E-01
t,y,yex= 0.2498E+01 0.8238E-01 0.8246E-01
t,y,yex= 0.2547E+01 0.7837E-01 0.7844E-01
t,y,yex= 0.2597E+01 0.7455E-01 0.7462E-01
t,y,yex= 0.2647E+01 0.7092E-01 0.7098E-01
t,y,yex= 0.2697E+01 0.6746E-01 0.6752E-01
t,y,yex= 0.2747E+01 0.6418E-01 0.6423E-01
t,y,yex= 0.2797E+01 0.6105E-01 0.6110E-01
t,y,yex= 0.2847E+01 0.5807E-01 0.5813E-01
t,y,yex= 0.2897E+01 0.5525E-01 0.5529E-01
t,y,yex= 0.2947E+01 0.5255E-01 0.5260E-01
t,y,yex= 0.2997E+01 0.4999E-01 0.5004E-01
t1,t2,dt= 0.000999000971 0.0316227786 0.000199800197
t,y,yex= 0.0000E+00 0.1000E+01 0.1001E+01
t,y,yex= 0.4995E-01 0.9522E+00 0.9532E+00
t,y,yex= 0.9990E-01 0.9059E+00 0.9067E+00
t,y,yex= 0.1499E+00 0.8617E+00 0.8626E+00
t,y,yex= 0.1998E+00 0.8198E+00 0.8205E+00
t,y,yex= 0.2498E+00 0.7798E+00 0.7806E+00
t,y,yex= 0.2997E+00 0.7418E+00 0.7425E+00
t,y,yex= 0.3497E+00 0.7057E+00 0.7063E+00
t,y,yex= 0.3996E+00 0.6713E+00 0.6719E+00
t,y,yex= 0.4496E+00 0.6386E+00 0.6392E+00
t,y,yex= 0.4995E+00 0.6075E+00 0.6080E+00
t,y,yex= 0.5495E+00 0.5779E+00 0.5784E+00
t,y,yex= 0.5994E+00 0.5497E+00 0.5502E+00
t,y,yex= 0.6494E+00 0.5229E+00 0.5234E+00
t,y,yex= 0.6993E+00 0.4974E+00 0.4979E+00
t,y,yex= 0.7493E+00 0.4732E+00 0.4737E+00
t,y,yex= 0.7992E+00 0.4502E+00 0.4506E+00
t,y,yex= 0.8492E+00 0.4282E+00 0.4286E+00
t,y,yex= 0.8991E+00 0.4074E+00 0.4078E+00
t,y,yex= 0.9491E+00 0.3875E+00 0.3879E+00
t,y,yex= 0.9990E+00 0.3686E+00 0.3690E+00
t,y,yex= 0.1049E+01 0.3507E+00 0.3510E+00
t,y,yex= 0.1099E+01 0.3336E+00 0.3339E+00
t,y,yex= 0.1149E+01 0.3173E+00 0.3176E+00
t,y,yex= 0.1199E+01 0.3019E+00 0.3022E+00
t,y,yex= 0.1249E+01 0.2872E+00 0.2874E+00
t,y,yex= 0.1299E+01 0.2732E+00 0.2734E+00
t,y,yex= 0.1349E+01 0.2599E+00 0.2601E+00
t,y,yex= 0.1399E+01 0.2472E+00 0.2474E+00
t,y,yex= 0.1449E+01 0.2352E+00 0.2354E+00
t,y,yex= 0.1499E+01 0.2237E+00 0.2239E+00
t,y,yex= 0.1548E+01 0.2128E+00 0.2130E+00
t,y,yex= 0.1598E+01 0.2024E+00 0.2026E+00
t,y,yex= 0.1648E+01 0.1926E+00 0.1928E+00
t,y,yex= 0.1698E+01 0.1832E+00 0.1834E+00
t,y,yex= 0.1748E+01 0.1743E+00 0.1744E+00
t,y,yex= 0.1798E+01 0.1658E+00 0.1659E+00
t,y,yex= 0.1848E+01 0.1577E+00 0.1578E+00
t,y,yex= 0.1898E+01 0.1500E+00 0.1502E+00
t,y,yex= 0.1948E+01 0.1427E+00 0.1428E+00
t,y,yex= 0.1998E+01 0.1358E+00 0.1359E+00
t,y,yex= 0.2048E+01 0.1291E+00 0.1293E+00
t,y,yex= 0.2098E+01 0.1228E+00 0.1230E+00
t,y,yex= 0.2148E+01 0.1169E+00 0.1170E+00
t,y,yex= 0.2198E+01 0.1112E+00 0.1113E+00
t,y,yex= 0.2248E+01 0.1058E+00 0.1058E+00
t,y,yex= 0.2298E+01 0.1006E+00 0.1007E+00
t,y,yex= 0.2348E+01 0.9570E-01 0.9578E-01
t,y,yex= 0.2398E+01 0.9104E-01 0.9112E-01
t,y,yex= 0.2448E+01 0.8660E-01 0.8668E-01
t,y,yex= 0.2498E+01 0.8238E-01 0.8246E-01
t,y,yex= 0.2547E+01 0.7837E-01 0.7844E-01
t,y,yex= 0.2597E+01 0.7455E-01 0.7462E-01
t,y,yex= 0.2647E+01 0.7092E-01 0.7098E-01
t,y,yex= 0.2697E+01 0.6746E-01 0.6752E-01
t,y,yex= 0.2747E+01 0.6418E-01 0.6423E-01
t,y,yex= 0.2797E+01 0.6105E-01 0.6110E-01
t,y,yex= 0.2847E+01 0.5807E-01 0.5813E-01
t,y,yex= 0.2897E+01 0.5525E-01 0.5529E-01
t,y,yex= 0.2947E+01 0.5255E-01 0.5260E-01
t,y,yex= 0.2997E+01 0.4999E-01 0.5004E-01