14 March 2012 01:24:33 PM

RKF45_PRB
  C++ version
  Test the RKF45 library.

TEST01
  Solve a scalar equation using R4_RKF:

  Y' = 0.25 * Y * ( 1 - Y / 20 )


FLAG             T          Y         Y'          Y_Exact         Error

   1             0             1        0.2375             1             0
   2             4        2.5032      0.547476       2.50322  -1.62125e-05
   2             8       5.60005       1.00801       5.60009  -3.95775e-05
   2            12       10.2781       1.24903       10.2777   0.000331879
   2            16       14.8368      0.957569       14.8368  -4.00543e-05
   2            20        17.731      0.502901       17.7302   0.000804901

TEST02
  Solve a vector equation using R4_RKF:

  Y'(1) =  Y(2)
  Y'(2) = -Y(1)


  This system is equivalent to the following
  second order system:

  Z" = - Z.

FLAG             T          Y(1)       Y(2)

   1             0             1             0
   2      0.523599      0.866026          -0.5
   2        1.0472      0.500016     -0.866037
   2        1.5708   1.51132e-05      -1.00004
   2        2.0944     -0.500007     -0.866082
   2       2.61799     -0.866071     -0.500061
   2       3.14159      -1.00009  -3.74492e-05
   2       3.66519     -0.866138      0.500013
   2       4.18879     -0.500106      0.866104
   2       4.71239  -5.98872e-05       1.00014
   2       5.23599       0.50002      0.866193
   2       5.75959      0.866138      0.500151
   2       6.28319       1.00019   8.20951e-05

TEST03
  Solve a scalar equation using R4_RKF:

  Y' = 0.25 * Y * ( 1 - Y / 20 )

  This routine uses the SINGLE STEP mode.


FLAG             T          Y         Y'        Y_Exact         Error

  -1             0             1        0.2375             1             0
  -2       0.31096       1.07649      0.254637       1.07649             0
  -2       1.86576        1.5483      0.357109        1.5483  -2.02656e-06
   2             4        2.5032      0.547476       2.50322  -1.62125e-05
  -2             6       3.81715      0.772154       3.81718  -2.95639e-05
   2             8       5.60005       1.00801       5.60009  -3.95775e-05
   2            12       10.2781       1.24903       10.2777   0.000331879
   2            16       14.8368      0.957569       14.8368  -4.00543e-05
   2            20        17.731      0.502901       17.7302   0.000804901

TEST04
  Solve a scalar equation using R8_RKF:

  Y' = 0.25 * Y * ( 1 - Y / 20 )


FLAG             T          Y         Y'          Y_Exact         Error

   1             0             1        0.2375             1             0
   8             0             1        0.2375             1             0
   8             4             1        0.2375       2.50322      -1.50322
   8             8             1        0.2375       5.60009      -4.60009
   8            12             1        0.2375       10.2777      -9.27773
   8            16             1        0.2375       14.8368      -13.8368

TEST05
  Solve a vector equation using R8_RKF:

  Y'(1) =  Y(2)
  Y'(2) = -Y(1)


FLAG             T          Y(1)       Y(2)

   1             0             1             0
   8             0             1             0
   8      0.523599             1             0
   8        1.0472             1             0
   8        1.5708             1             0
   8        2.0944             1             0
   8       2.61799             1             0
   8       3.14159             1             0
   8       3.66519             1             0
   8       4.18879             1             0
   8       4.71239             1             0
   8       5.23599             1             0
   8       5.75959             1             0

TEST06
  Solve a scalar equation using R8_RKF:

  Y' = 0.25 * Y * ( 1 - Y / 20 )

  This routine uses the SINGLE STEP mode.


FLAG             T          Y         Y'        Y_Exact         Error

  -1             0             1        0.2375             1             0
   8             0             1        0.2375             1             0
   8             4             1        0.2375       2.50322      -1.50322
   8             8             1        0.2375       5.60009      -4.60009
   8            12             1        0.2375       10.2777      -9.27773
   8            16             1        0.2375       14.8368      -13.8368

RKF45_PRB
  Normal end of execution.

14 March 2012 01:24:33 PM