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Harmonic Oscillator 2

Equations:
Description:

Derived from a second order linear equation with circular solution trajectories.

Keywords:

periodic; min test set

Plots:

Initial value problems:

IVP 50

Class: PILAU

Exact Solution*:
View test data:
Solver
Settings
Results
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=0.24810
  • c5: t_us=0.24730 ,  e_us=2.998254977626402e-10
  • c6: t_bd=10.000000 ,  e_bd=6.457304559948085e-07
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 1
  • c4: t_c=0.49970
  • c5: t_us=0.49760 ,  e_us=2.998254977626402e-10
  • c6: t_bd=10.000000 ,  e_bd=6.457304559948085e-07
DynIbex
  • arithmetic: Interval
  • method: 9
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=0.82800
  • c5: t_us=0.82470 ,  e_us=2.906941228047577e-02
  • c6: t_bd=10.000000 ,  e_bd=1.649499004799545e+00
DynIbex
  • arithmetic: Interval
  • method: 11
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=1.73510
  • c5: t_us=1.73070 ,  e_us=4.931604801944034e-02
  • c6: t_bd=10.000000 ,  e_bd=3.929374703484965e+00
VNODE-LP
  • method: HOE
  • order: 10
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.00400
  • c5: t_us=0.00160 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 15
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.00800
  • c5: t_us=0.00470 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 20
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.01200
  • c5: t_us=0.00740 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 5
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.02410
  • c5: t_us=0.01750 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
Generate graphics:

IVP 51

Class: PILANU

Exact Solution*:
View test data:
Solver
Settings
Results
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=0.23890
  • c5: t_us=0.23600 ,  e_us=1.747268996155071e-12
  • c6: t_bd=10.000000 ,  e_bd=2.377741026293734e-08
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 1
  • c4: t_c=0.62110
  • c5: t_us=0.61780 ,  e_us=1.747268996155071e-12
  • c6: t_bd=10.000000 ,  e_bd=2.377741026293734e-08
DynIbex
  • arithmetic: Interval
  • method: 9
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=0.94440
  • c5: t_us=0.93990 ,  e_us=1e-308
  • c6: t_bd=10.000000 ,  e_bd=1.446625053080908e-08
DynIbex
  • arithmetic: Interval
  • method: 11
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=1.85710
  • c5: t_us=1.85200 ,  e_us=7.823741654533478e-13
  • c6: t_bd=10.000000 ,  e_bd=8.741652846033787e-09
VNODE-LP
  • method: HOE
  • order: 10
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.00400
  • c5: t_us=0.00260 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 15
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.00800
  • c5: t_us=0.00540 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 20
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.01190
  • c5: t_us=0.00730 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 5
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.02650
  • c5: t_us=0.02040 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
Generate graphics:

IVP 74

Class: PILAU

Exact Solution*:
View test data:
Solver
Settings
Results
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=0.23790
  • c5: t_us=0.23770 ,  e_us=3.523425995410889e-11
  • c6: t_bd=10.000000 ,  e_bd=3.477994303668908e-07
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 1
  • c4: t_c=0.63040
  • c5: t_us=0.62740 ,  e_us=3.523425995410889e-11
  • c6: t_bd=10.000000 ,  e_bd=3.477994303668908e-07
DynIbex
  • arithmetic: Interval
  • method: 9
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=0.95160
  • c5: t_us=0.94640 ,  e_us=2.975130260526759e-03
  • c6: t_bd=10.000000 ,  e_bd=1.201487430338097e-01
DynIbex
  • arithmetic: Interval
  • method: 11
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=1.88300
  • c5: t_us=1.87660 ,  e_us=4.980225156152818e-03
  • c6: t_bd=10.000000 ,  e_bd=3.652610998296274e-01
VNODE-LP
  • method: HOE
  • order: 10
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.00400
  • c5: t_us=0.00280 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 15
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.00790
  • c5: t_us=0.00430 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 20
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.01190
  • c5: t_us=0.00670 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
VNODE-LP
  • method: HOE
  • order: 5
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.02810
  • c5: t_us=0.02230 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
Generate graphics:

* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.

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