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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 = 129
CVode integer workspace length = 60
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 = 129
CVode integer workspace length = 60
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 = 129
CVode integer workspace length = 60
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 = 129
CVode integer workspace length = 60
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 = 115
CVode integer workspace length = 53
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 = 115
CVode integer workspace length = 53
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 = 115
CVode integer workspace length = 53
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 = 115
CVode integer workspace length = 53
Number of steps = 266
Number of f-s = 359
Number of setups = 39
Number of nonlinear iterations = 356
Number of nonlinear convergence failures = 1
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
-------------------------------------------------------------
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 = 589
CVode integer workspace length = 60
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 = 589
CVode integer workspace length = 60
Number of steps = 154
Number of f-s = 218
Number of setups = 33
Number of nonlinear iterations = 215
Number of nonlinear convergence failures = 4
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 = 589
CVode integer workspace length = 60
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 = 589
CVode integer workspace length = 60
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 = 414
CVode integer workspace length = 53
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 = 414
CVode integer workspace length = 53
Number of steps = 180
Number of f-s = 270
Number of setups = 47
Number of nonlinear iterations = 267
Number of nonlinear convergence failures = 12
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 = 414
CVode integer workspace length = 53
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 = 414
CVode integer workspace length = 53
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
|
