June 20 2002   9:29:07.085 AM
 
RKF45_PRB
  Demonstrate the RKF45 ODE integrator.
 
TEST01
  Solve a scalar equation:
 
  Y' = 0.25 * Y * ( 1 - Y / 20 )
 
 
       T          Y         Y_Exact         Error
 
   0.00000       1.00000       1.00000       0.00000    
   4.00000       2.50322       2.50322     -0.452995E-05
   8.00000       5.60008       5.60009     -0.109673E-04
   12.0000       10.2777       10.2777     -0.123978E-04
   16.0000       14.8368       14.8368     -0.953674E-05
   20.0000       17.7302       17.7302       0.00000    
 
TEST02
  Solve a vector equation:
 
  Y'(1) =   Y(2)
  Y'(2) = - Y(1)
 
 
       T          Y
 
   0.00000       1.00000       0.00000    
  0.523599      0.866026     -0.500000    
   1.04720      0.500002     -0.866027    
   1.57080      0.596046E-06  -1.00000    
   2.09440     -0.500001     -0.866028    
   2.61799     -0.866028     -0.500002    
   3.14159      -1.00001     -0.923872E-06
   3.66519     -0.866031      0.500002    
   4.18879     -0.500004      0.866031    
   4.71239     -0.116229E-05   1.00001    
   5.23599      0.500003      0.866032    
   5.75959      0.866032      0.500005    
   6.28319       1.00001      0.819564E-06
 
TEST03
  Solve a scalar equation in double precision:
 
  Y' = 0.25 * Y * ( 1 - Y / 20 )
 
 
       T          Y         Y_Exact         Error
 
   0.00000       1.00000       1.00000       0.00000    
   4.00000       2.50322       2.50322     -0.135049E-08
   8.00000       5.60009       5.60009     -0.372025E-08
   12.0000       10.2777       10.2777      0.248324E-09
   16.0000       14.8368       14.8368     -0.957398E-08
   20.0000       17.7302       17.7302     -0.139216E-08
 
TEST04
  Solve a vector equation in double precision:
 
  Y'(1) =   Y(2)
  Y'(2) = - Y(1)
 
 
       T          Y
 
   0.00000       1.00000       0.00000    
  0.523599      0.866025     -0.500000    
   1.04720      0.500000     -0.866025    
   1.57080      0.183435E-08  -1.00000    
   2.09440     -0.500000     -0.866025    
   2.61799     -0.866025     -0.500000    
   3.14159      -1.00000     -0.366759E-08
   3.66519     -0.866025      0.500000    
   4.18879     -0.500000      0.866025    
   4.71239     -0.550444E-08   1.00000    
   5.23599      0.500000      0.866025    
   5.75959      0.866025      0.500000    
   6.28319       1.00000      0.734112E-08
 
RKF45_PRB
  Normal end of execution.