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Oil reservoir problem

Equations:
Description:

A stiff problem with par0 as the stiffness coefficient (the smaller, the stiffer).

Keywords:

non-periodic; stiff; min test set

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Plots:

Initial value problems:

IVP 73

Class: PIINLANU

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=0.15140
  • c5: t_us=0.15110 ,  e_us=4.620675412972397e-06
  • c6: t_bd=10.000000 ,  e_bd=1.049753680759657e-06
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 1
  • c4: t_c=0.79390
  • c5: t_us=0.79100 ,  e_us=4.620675963171172e-06
  • c6: t_bd=10.000000 ,  e_bd=1.049751415183042e-06
DynIbex
  • arithmetic: Interval
  • method: 9
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=1.22530
  • c5: t_us=1.22160 ,  e_us=1.127182549381933e-08
  • c6: t_bd=10.000000 ,  e_bd=2.652641051259508e-09
DynIbex
  • arithmetic: Interval
  • method: 11
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=2.98870
  • c5: t_us=2.97940 ,  e_us=8.398724778146960e-09
  • c6: t_bd=10.000000 ,  e_bd=2.019625466864738e-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=0.00170 ,  e_us=1.047772979489991e-15
  • c6: t_bd=10.000000 ,  e_bd=2.408628851924277e-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=0.00400 ,  e_us=9.020562075079397e-17
  • c6: t_bd=10.000000 ,  e_bd=1.222744128170916e-12
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=0.00630 ,  e_us=4.163336342344337e-17
  • c6: t_bd=10.000000 ,  e_bd=6.316336342848672e-13
VNODE-LP
  • method: HOE
  • order: 5
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.01790
  • c5: t_us=0.01100 ,  e_us=1.209796152146225e-14
  • c6: t_bd=10.000000 ,  e_bd=4.150291221804991e-13
Generate graphics:
DynIbex VNODE-LP
WPD for Problem 73

IVP 104

Class: PIINLANU

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=0.14400
  • c5: t_us=0.14320 ,  e_us=4.622579796761950e-06
  • c6: t_bd=10.000000 ,  e_bd=1.050181377859616e-06
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 1
  • c4: t_c=0.82830
  • c5: t_us=0.82590 ,  e_us=4.622580346967664e-06
  • c6: t_bd=10.000000 ,  e_bd=1.050179112560556e-06
DynIbex
  • arithmetic: Interval
  • method: 9
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=1.25970
  • c5: t_us=1.25580 ,  e_us=7.179934854995018e-09
  • c6: t_bd=10.000000 ,  e_bd=1.692451512269599e-09
DynIbex
  • arithmetic: Interval
  • method: 11
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=3.01920
  • c5: t_us=3.01330 ,  e_us=6.026037252526706e-09
  • c6: t_bd=10.000000 ,  e_bd=1.451993414391950e-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=0.00210 ,  e_us=1.051242426441945e-15
  • c6: t_bd=10.000000 ,  e_bd=2.401689958020370e-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=0.00500 ,  e_us=8.673617379884035e-17
  • c6: t_bd=10.000000 ,  e_bd=1.223104950653919e-12
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=0.00740 ,  e_us=3.816391647148976e-17
  • c6: t_bd=10.000000 ,  e_bd=6.315503675580203e-13
VNODE-LP
  • method: HOE
  • order: 5
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.01780
  • c5: t_us=0.01150 ,  e_us=1.209449207451030e-14
  • c6: t_bd=10.000000 ,  e_bd=4.150291221804991e-13
Generate graphics:
DynIbex VNODE-LP
WPD for Problem 104

IVP 105

Class: PIINLANU

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=0.15510
  • c5: t_us=0.15380 ,  e_us=4.641636992715192e-06
  • c6: t_bd=10.000000 ,  e_bd=1.054462734240147e-06
DynIbex
  • arithmetic: Interval
  • method: 7
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 1
  • c4: t_c=0.84240
  • c5: t_us=0.84030 ,  e_us=4.641637542879273e-06
  • c6: t_bd=10.000000 ,  e_bd=1.054460471328067e-06
DynIbex
  • arithmetic: Interval
  • method: 9
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=1.28000
  • c5: t_us=1.27450 ,  e_us=2.644581283128833e-09
  • c6: t_bd=10.000000 ,  e_bd=6.283168429987995e-10
DynIbex
  • arithmetic: Interval
  • method: 11
  • abs. tolerance: 1e-12
  • initial stepsize: 1e-3
  • min. stepsize: 1e-5
  • monotonicity: 0
  • c4: t_c=3.03280
  • c5: t_us=3.02450 ,  e_us=2.061037757128403e-09
  • c6: t_bd=10.000000 ,  e_bd=5.035414307741348e-10
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=0.00200 ,  e_us=1.044303532538038e-15
  • c6: t_bd=10.000000 ,  e_bd=2.402245069532682e-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=0.00520 ,  e_us=8.673617379884035e-17
  • c6: t_bd=10.000000 ,  e_bd=1.224159662527313e-12
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=0.00770 ,  e_us=3.469446951953614e-17
  • c6: t_bd=10.000000 ,  e_bd=6.321054790703329e-13
VNODE-LP
  • method: HOE
  • order: 5
  • abs. tolerance: 1e-12
  • rel. tolerance: 1e-12
  • min. stepsize: 1e-05
  • c4: t_c=0.01770
  • c5: t_us=0.01140 ,  e_us=1.269817584415023e-14
  • c6: t_bd=10.000000 ,  e_bd=4.130584763117895e-13
Generate graphics:
DynIbex VNODE-LP
WPD for Problem 105

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

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