Demonstration program for CVODE package - direct linear solvers


Problem 1: Van der Pol oscillator
 xdotdot - 3*(1 - x^2)*xdot + x = 0, x(0) = 2, xdot(0) = 0
 neq = 2,  reltol = 0,  abstol = 1e-06

-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : FIXEDPOINT

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91056e-01    5    9.8626e-02
   3.60761    -2.12391e-05   -3.16877e+00    5    2.2757e-02
   5.82239    -1.68010e+00    2.91060e-01    4    1.4079e-01
   8.03716     9.57608e-05    3.16900e+00    5    2.0348e-02

 Final statistics for this run:

 CVode real workspace length              =  136 
 CVode integer workspace length           =   72 
 Number of steps                          =  196 
 Number of f-s                            =  390 
 Number of setups                         =    0 
 Number of nonlinear iterations           =  387 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   15 

 Error overrun = 95.761 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : NEWTON
Linear Solver           : Dense, User-Supplied Jacobian

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91056e-01    7    6.5178e-02
   3.60761     2.42943e-06   -3.16870e+00    7    2.0626e-02
   5.82239    -1.68010e+00    2.91062e-01    7    1.3038e-01
   8.03716     1.99078e-05    3.16879e+00    7    2.3923e-02

 Final statistics for this run:

 CVode real workspace length              =  136 
 CVode integer workspace length           =   72 
 Number of steps                          =  266 
 Number of f-s                            =  365 
 Number of setups                         =   46 
 Number of nonlinear iterations           =  362 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   23 

 Linear solver real workspace length      =   10 
 Linear solver integer workspace length   =   41 
 Number of Jacobian evaluations           =    5 
 Number of f evals. in linear solver      =    0 

 Error overrun = 19.908 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : NEWTON
Linear Solver           : Dense, Difference Quotient Jacobian

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91056e-01    5    6.5835e-02
   3.60761    -2.28046e-05   -3.16879e+00    6    3.1773e-02
   5.82239    -1.68010e+00    2.91059e-01    6    9.3514e-02
   8.03716    -9.84742e-06    3.16869e+00    6    2.8096e-02

 Final statistics for this run:

 CVode real workspace length              =  136 
 CVode integer workspace length           =   72 
 Number of steps                          =  195 
 Number of f-s                            =  267 
 Number of setups                         =   34 
 Number of nonlinear iterations           =  264 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   15 

 Linear solver real workspace length      =   10 
 Linear solver integer workspace length   =   41 
 Number of Jacobian evaluations           =    4 
 Number of f evals. in linear solver      =    8 

 Error overrun = 22.805 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : NEWTON
Linear Solver           : Diagonal Jacobian

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91054e-01    6    5.9553e-02
   3.60761     6.36071e-05   -3.16853e+00    6    2.8912e-02
   5.82239    -1.68011e+00    2.91057e-01    5    9.8149e-02
   8.03716    -7.70359e-05    3.16847e+00    6    2.3224e-02

 Final statistics for this run:

 CVode real workspace length              =  136 
 CVode integer workspace length           =   72 
 Number of steps                          =  238 
 Number of f-s                            =  329 
 Number of setups                         =   40 
 Number of nonlinear iterations           =  326 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   20 

 Linear solver real workspace length      =    6 
 Linear solver integer workspace length   =    3 
 Number of Jacobian evaluations           =   40 
 Number of f evals. in linear solver      =   40 

 Error overrun = 77.036 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : FIXEDPOINT

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91056e-01    4    9.6100e-02
   3.60761    -1.35636e-04   -3.16912e+00    5    1.5675e-02
   5.82239    -1.68009e+00    2.91063e-01    5    1.1210e-01
   8.03716     2.20969e-04    3.16937e+00    5    1.4732e-02

 Final statistics for this run:

 CVode real workspace length              =  122 
 CVode integer workspace length           =   65 
 Number of steps                          =  262 
 Number of f-s                            =  497 
 Number of setups                         =    0 
 Number of nonlinear iterations           =  494 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   22 

 Error overrun = 220.969 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : NEWTON
Linear Solver           : Dense, User-Supplied Jacobian

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91056e-01    5    1.1991e-01
   3.60761    -5.46907e-05   -3.16886e+00    5    1.6403e-02
   5.82239    -1.68010e+00    2.91061e-01    4    1.0146e-01
   8.03716     1.54312e-04    3.16917e+00    4    9.5378e-03

 Final statistics for this run:

 CVode real workspace length              =  122 
 CVode integer workspace length           =   65 
 Number of steps                          =  265 
 Number of f-s                            =  357 
 Number of setups                         =   40 
 Number of nonlinear iterations           =  354 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   18 

 Linear solver real workspace length      =   10 
 Linear solver integer workspace length   =   41 
 Number of Jacobian evaluations           =    5 
 Number of f evals. in linear solver      =    0 

 Error overrun = 154.312 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : NEWTON
Linear Solver           : Dense, Difference Quotient Jacobian

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91058e-01    4    8.1067e-02
   3.60761    -5.84200e-05   -3.16886e+00    4    1.1360e-02
   5.82239    -1.68010e+00    2.91062e-01    5    6.4941e-02
   8.03716     9.61737e-05    3.16899e+00    5    1.5216e-02

 Final statistics for this run:

 CVode real workspace length              =  122 
 CVode integer workspace length           =   65 
 Number of steps                          =  276 
 Number of f-s                            =  366 
 Number of setups                         =   40 
 Number of nonlinear iterations           =  363 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   17 

 Linear solver real workspace length      =   10 
 Linear solver integer workspace length   =   41 
 Number of Jacobian evaluations           =    6 
 Number of f evals. in linear solver      =   12 

 Error overrun = 96.174 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : NEWTON
Linear Solver           : Diagonal Jacobian

     t           x              xdot         qu     hu 
   1.39284     1.68010e+00   -2.91056e-01    5    1.1430e-01
   3.60761    -9.83501e-05   -3.16900e+00    5    1.6712e-02
   5.82239    -1.68009e+00    2.91063e-01    4    8.1261e-02
   8.03716     1.66640e-04    3.16920e+00    4    1.0546e-02

 Final statistics for this run:

 CVode real workspace length              =  122 
 CVode integer workspace length           =   65 
 Number of steps                          =  266 
 Number of f-s                            =  359 
 Number of setups                         =   39 
 Number of nonlinear iterations           =  356 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =   17 

 Linear solver real workspace length      =    6 
 Linear solver integer workspace length   =    3 
 Number of Jacobian evaluations           =   39 
 Number of f evals. in linear solver      =   39 

 Error overrun = 166.640 


-------------------------------------------------------------
-------------------------------------------------------------

Problem 2: ydot = A * y, where A is a banded lower
triangular matrix derived from 2-D advection PDE

 neq = 25, ml = 5, mu = 0
 itol = CV_SS, reltol = 0, abstol = 1e-06
      t        max.err      qu     hu 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : FIXEDPOINT

      t        max.err      qu     hu 
     0.010    1.4690e-07    3     1.1459e-02
     0.100    5.2543e-07    4     4.1413e-02
     1.000    1.2207e-06    5     6.8243e-02
    10.000    9.7711e-07    3     2.8481e-01
   100.000    2.2510e-07    1     6.7722e-01

 Final statistics for this run:

 CVode real workspace length              =  596 
 CVode integer workspace length           =   72 
 Number of steps                          =  341 
 Number of f-s                            =  601 
 Number of setups                         =    0 
 Number of nonlinear iterations           =  598 
 Number of nonlinear convergence failures =   79 
 Number of error test failures            =    0 

 Error overrun = 1.221 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : NEWTON
Linear Solver           : Diagonal Jacobian

      t        max.err      qu     hu 
     0.010    1.3734e-07    3     1.0327e-02
     0.100    2.4956e-06    3     2.3048e-02
     1.000    4.2328e-06    4     4.3778e-02
    10.000    9.7303e-07    4     3.1286e-01
   100.000    1.1241e-09    1     3.7371e+02

 Final statistics for this run:

 CVode real workspace length              =  596 
 CVode integer workspace length           =   72 
 Number of steps                          =  154 
 Number of f-s                            =  218 
 Number of setups                         =   33 
 Number of nonlinear iterations           =  215 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =    5 

 Linear solver real workspace length      =   75 
 Linear solver integer workspace length   =    3 
 Number of Jacobian evaluations           =   33 
 Number of f evals. in linear solver      =   33 

 Error overrun = 4.233 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : NEWTON
Linear Solver           : Band, User-Supplied Jacobian

      t        max.err      qu     hu 
     0.010    1.3670e-07    3     1.2164e-02
     0.100    4.7920e-07    4     4.2115e-02
     1.000    2.5077e-07    6     1.0365e-01
    10.000    6.0790e-07    4     4.7206e-01
   100.000    5.7390e-08    2     1.0750e+01

 Final statistics for this run:

 CVode real workspace length              =  596 
 CVode integer workspace length           =   72 
 Number of steps                          =  149 
 Number of f-s                            =  183 
 Number of setups                         =   32 
 Number of nonlinear iterations           =  180 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =    6 

 Linear solver real workspace length      =  327 
 Linear solver integer workspace length   =   91 
 Number of Jacobian evaluations           =    3 
 Number of f evals. in linear solver      =    0 

 Error overrun = 0.608 


-------------------------------------------------------------

Linear Multistep Method : ADAMS
Iteration               : NEWTON
Linear Solver           : Band, Difference Quotient Jacobian

      t        max.err      qu     hu 
     0.010    1.4285e-07    3     1.3840e-02
     0.100    5.7337e-07    4     4.2111e-02
     1.000    7.3281e-07    5     6.3684e-02
    10.000    3.8507e-07    5     2.6026e-01
   100.000    4.1037e-12    1     6.2591e+01

 Final statistics for this run:

 CVode real workspace length              =  596 
 CVode integer workspace length           =   72 
 Number of steps                          =  124 
 Number of f-s                            =  141 
 Number of setups                         =   24 
 Number of nonlinear iterations           =  138 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =    1 

 Linear solver real workspace length      =  327 
 Linear solver integer workspace length   =   91 
 Number of Jacobian evaluations           =    3 
 Number of f evals. in linear solver      =   18 

 Error overrun = 0.733 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : FIXEDPOINT

      t        max.err      qu     hu 
     0.010    5.5931e-07    2     8.1257e-03
     0.100    5.2896e-06    3     1.7769e-02
     1.000    2.3209e-06    5     7.5291e-02
    10.000    1.2861e-06    5     2.7791e-01
   100.000    2.8424e-07    1     2.5672e-01

 Final statistics for this run:

 CVode real workspace length              =  421 
 CVode integer workspace length           =   65 
 Number of steps                          =  372 
 Number of f-s                            =  692 
 Number of setups                         =    0 
 Number of nonlinear iterations           =  689 
 Number of nonlinear convergence failures =   56 
 Number of error test failures            =    1 

 Error overrun = 5.290 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : NEWTON
Linear Solver           : Diagonal Jacobian

      t        max.err      qu     hu 
     0.010    5.6365e-07    2     8.1241e-03
     0.100    7.9753e-07    4     1.8910e-02
     1.000    5.9100e-06    5     5.1976e-02
    10.000    2.1547e-06    4     3.1113e-01
   100.000    4.2213e-09    1     1.3897e+02

 Final statistics for this run:

 CVode real workspace length              =  421 
 CVode integer workspace length           =   65 
 Number of steps                          =  180 
 Number of f-s                            =  270 
 Number of setups                         =   47 
 Number of nonlinear iterations           =  267 
 Number of nonlinear convergence failures =    2 
 Number of error test failures            =    5 

 Linear solver real workspace length      =   75 
 Linear solver integer workspace length   =    3 
 Number of Jacobian evaluations           =   47 
 Number of f evals. in linear solver      =   47 

 Error overrun = 5.910 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : NEWTON
Linear Solver           : Band, User-Supplied Jacobian

      t        max.err      qu     hu 
     0.010    5.6372e-07    2     8.1246e-03
     0.100    5.2784e-06    3     1.7819e-02
     1.000    1.8169e-06    5     6.0110e-02
    10.000    5.4997e-07    5     4.1661e-01
   100.000    1.7764e-09    2     2.9748e+01

 Final statistics for this run:

 CVode real workspace length              =  421 
 CVode integer workspace length           =   65 
 Number of steps                          =  119 
 Number of f-s                            =  143 
 Number of setups                         =   25 
 Number of nonlinear iterations           =  140 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =    2 

 Linear solver real workspace length      =  327 
 Linear solver integer workspace length   =   91 
 Number of Jacobian evaluations           =    3 
 Number of f evals. in linear solver      =    0 

 Error overrun = 5.278 


-------------------------------------------------------------

Linear Multistep Method : BDF
Iteration               : NEWTON
Linear Solver           : Band, Difference Quotient Jacobian

      t        max.err      qu     hu 
     0.010    5.6492e-07    2     8.1361e-03
     0.100    5.9968e-06    3     1.7105e-02
     1.000    1.6902e-06    5     8.7628e-02
    10.000    5.2314e-07    5     3.1091e-01
   100.000    1.4380e-09    2     2.1635e+01

 Final statistics for this run:

 CVode real workspace length              =  421 
 CVode integer workspace length           =   65 
 Number of steps                          =  121 
 Number of f-s                            =  144 
 Number of setups                         =   24 
 Number of nonlinear iterations           =  141 
 Number of nonlinear convergence failures =    0 
 Number of error test failures            =    1 

 Linear solver real workspace length      =  327 
 Linear solver integer workspace length   =   91 
 Number of Jacobian evaluations           =    3 
 Number of f evals. in linear solver      =   18 

 Error overrun = 5.997 


-------------------------------------------------------------
-------------------------------------------------------------

 Number of errors encountered = 0 
