18 March 2012  11:44:03.883 AM
 
PCE_ODE_HERMITE_TEST:
  FORTRAN90 version
  Test PCE_ODE_HERMITE.
 
PCE_ODE_HERMITE_TEST01:
  Call PCE_ODE_HERMITE to compute a polynomial chaos expansion
  for the ODE:
 
    u' = - alpha * u,
    u(0) = 1.
 
  Initial time         TI =    0.00000    
  Final time           TF =    2.00000    
  Number of time steps NT =    200
  Initial condition    UI =    1.00000    
  Expansion degree     NP =      4
  E(ALPHA)       ALPHA_MU =    0.00000    
  STD(ALPHA)  ALPHA_SIGMA =    1.00000    
 
 i  T(i)  E(U(T(i)))    U(T(i),0)
 
     0   0.000     1.00000         1.00000         0.00000    
    10   0.100     1.00501         1.00451        0.506218E-03
    20   0.200     1.02020         1.01915        0.105541E-02
    30   0.300     1.04603         1.04433        0.169674E-02
    40   0.400     1.08329         1.08080        0.248698E-02
    50   0.500     1.13315         1.12965        0.349537E-02
    60   0.600     1.19722         1.19241        0.480986E-02
    70   0.700     1.27762         1.27108        0.654525E-02
    80   0.800     1.37713         1.36827        0.885450E-02
    90   0.900     1.49930         1.48736        0.119446E-01
   100   1.000     1.64872         1.63262        0.160997E-01
   110   1.100     1.83125         1.80954        0.217156E-01
   120   1.200     2.05443         2.02508        0.293505E-01
   130   1.300     2.32798         2.28817        0.398037E-01
   140   1.400     2.66446         2.61022        0.542352E-01
   150   1.500     3.08022         3.00587        0.743494E-01
   160   1.600     3.59664         3.49396        0.102681    
   170   1.700     4.24185         4.09882        0.143035    
   180   1.800     5.05309         4.85192        0.201174    
   190   1.900     6.07997         5.79409        0.285881    
   200   2.000     7.38906         6.97844        0.410611    
 
PCE_ODE_HERMITE_TEST02:
  Examine convergence behavior as the PCE degree increases:
 
    u' = - alpha * u,
    u(0) = 1.
 
  Initial time         TI =    0.00000    
  Final time           TF =    2.00000    
  Number of time steps NT =   2000
  Initial condition    UI =    1.00000    
  E(ALPHA)       ALPHA_MU =    0.00000    
  STD(ALPHA)  ALPHA_SIGMA =    1.00000    
 
    NP     Error(NP)     Log(Error(NP))
 
     0     6.38906         1.85459    
     1     3.63062         1.28940    
     2     1.40850        0.342522    
     3    0.421433       -0.864094    
     4    0.121242        -2.10997    
     5    0.519274E-01    -2.95791    
 
PCE_ODE_HERMITE_TEST:
  Normal end of execution.
 
18 March 2012  11:44:03.891 AM