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, itol = CV_SS, reltol = 0, abstol = 1e-06 ------------------------------------------------------------- Linear Multistep Method : ADAMS Iteration : FUNCTIONAL t x xdot qu hu 1.39284 1.68010e+00 -2.91056e-01 5 9.8626e-02 3.60761 -2.12392e-05 -3.16877e+00 5 2.2756e-02 5.82239 -1.68010e+00 2.91060e-01 4 1.4079e-01 8.03716 9.57611e-05 3.16900e+00 5 2.0348e-02 Final statistics for this run: CVode real workspace length = 130 CVode integer workspace length = 69 Number of steps = 196 Number of f-s = 391 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 = 130 CVode integer workspace length = 69 Number of steps = 266 Number of f-s = 366 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 = 8 Linear solver integer workspace length = 2 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 -9.84768e-06 3.16869e+00 6 2.8096e-02 Final statistics for this run: CVode real workspace length = 130 CVode integer workspace length = 69 Number of steps = 195 Number of f-s = 268 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 = 8 Linear solver integer workspace length = 2 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 9.8123e-02 8.03716 -8.21358e-05 3.16848e+00 6 2.2328e-02 Final statistics for this run: CVode real workspace length = 130 CVode integer workspace length = 69 Number of steps = 241 Number of f-s = 340 Number of setups = 42 Number of nonlinear iterations = 336 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 = 42 Number of f evals. in linear solver = 42 Error overrun = 82.136 ------------------------------------------------------------- Linear Multistep Method : BDF Iteration : FUNCTIONAL 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 = 116 CVode integer workspace length = 62 Number of steps = 262 Number of f-s = 498 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 = 116 CVode integer workspace length = 62 Number of steps = 265 Number of f-s = 358 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 = 8 Linear solver integer workspace length = 2 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 = 116 CVode integer workspace length = 62 Number of steps = 276 Number of f-s = 367 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 = 8 Linear solver integer workspace length = 2 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 1.66644e-04 3.16920e+00 4 1.0547e-02 Final statistics for this run: CVode real workspace length = 116 CVode integer workspace length = 62 Number of steps = 266 Number of f-s = 360 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 = 166.644 ------------------------------------------------------------- ------------------------------------------------------------- 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 : FUNCTIONAL 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 1.5230e-07 1 6.0816e-01 Final statistics for this run: CVode real workspace length = 521 CVode integer workspace length = 69 Number of steps = 341 Number of f-s = 601 Number of setups = 0 Number of nonlinear iterations = 597 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 9.7335e-07 4 3.1286e-01 100.000 8.2265e-10 1 3.9630e+02 Final statistics for this run: CVode real workspace length = 521 CVode integer workspace length = 69 Number of steps = 154 Number of f-s = 219 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 = 521 CVode integer workspace length = 69 Number of steps = 149 Number of f-s = 184 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 = 425 Linear solver integer workspace length = 25 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 4.1035e-12 1 6.2591e+01 Final statistics for this run: CVode real workspace length = 521 CVode integer workspace length = 69 Number of steps = 124 Number of f-s = 142 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 = 425 Linear solver integer workspace length = 25 Number of Jacobian evaluations = 3 Number of f evals. in linear solver = 18 Error overrun = 0.733 ------------------------------------------------------------- Linear Multistep Method : BDF Iteration : FUNCTIONAL 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 1.6770e-08 1 8.7560e-01 Final statistics for this run: CVode real workspace length = 346 CVode integer workspace length = 62 Number of steps = 377 Number of f-s = 698 Number of setups = 0 Number of nonlinear iterations = 694 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 1.1253e-05 4 9.7523e-02 100.000 1.1182e-09 1 8.7300e+01 Final statistics for this run: CVode real workspace length = 346 CVode integer workspace length = 62 Number of steps = 202 Number of f-s = 315 Number of setups = 63 Number of nonlinear iterations = 311 Number of nonlinear convergence failures = 5 Number of error test failures = 7 Linear solver real workspace length = 75 Linear solver integer workspace length = 3 Number of Jacobian evaluations = 63 Number of f evals. in linear solver = 63 Error overrun = 11.253 ------------------------------------------------------------- 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 = 346 CVode integer workspace length = 62 Number of steps = 119 Number of f-s = 144 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 = 425 Linear solver integer workspace length = 25 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 = 346 CVode integer workspace length = 62 Number of steps = 121 Number of f-s = 145 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 = 425 Linear solver integer workspace length = 25 Number of Jacobian evaluations = 3 Number of f evals. in linear solver = 18 Error overrun = 5.997 ------------------------------------------------------------- ------------------------------------------------------------- Number of errors encountered = 0