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