A1 DETEST

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Equations:

$$\begin{align}\dot{x}_{0}&=- par_{0} \cdot x_{0}\end{align}$$

Description:

A very simple linear ODE.
Link to DETEST description

Keywords:

min test set

Download file

Plots:

C5 WPD

Initial value problems:

1 (PILANU)
2 (PILANU) [untested]
9 (PILAU)
70 (PILAU)
71 (PILAU)
81 (PILANU) [untested]
82 (PILAU) [untested]

IVP 1

Class: PILANU

Initial conditions:

$$\begin{align}x_{0}(0)&=1.0\end{align}$$

Parameter:

$$\begin{align}par_{0}&=1.0\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&=1.0 \cdot e^{- 1.0 \cdot t}\end{align}$$

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=0.03120
c5: t_us=0.03000 , e_us=7.827627435119666e-13
c6: t_bd=10.000000 , e_bd=7.487506640635293e-13

DynIbex

arithmetic: Interval
method: 7
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 1

c4: t_c=0.07460
c5: t_us=0.07220 , e_us=7.827627435119666e-13
c6: t_bd=10.000000 , e_bd=7.487506640635293e-13

DynIbex

arithmetic: Interval
method: 9
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.09940
c5: t_us=0.09590 , e_us=5.105360578738782e-13
c6: t_bd=10.000000 , e_bd=4.812150095176611e-13

DynIbex

arithmetic: Interval
method: 11
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.12410
c5: t_us=0.11900 , e_us=4.296007993787043e-13
c6: t_bd=10.000000 , e_bd=3.852860074710605e-13

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=1.4432899320127e-15
c6: t_bd=10 , e_bd=5.27403370541996e-16

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=0.00330 , e_us=1e-308
c6: t_bd=10 , e_bd=8.35513299171642e-18

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=0.00650 , e_us=1e-308
c6: t_bd=10 , e_bd=8.470329472543e-19

VNODE-LP

method: HOE
order: 5
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.02060
c5: t_us=0.01370 , e_us=4.70179450928754e-14
c6: t_bd=10 , e_bd=2.15332715850988e-15

Generate graphics:

DynIbex VNODE-LP

WPD for Problem 1

IVP 2

Class: PILANU

Initial conditions:

$$\begin{align}x_{0}(0)&=2.0\end{align}$$

Parameter:

$$\begin{align}par_{0}&=0.5\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&=2.0 \cdot e^{- 0.5 \cdot t}\end{align}$$

[untested]

IVP 9

Class: PILAU

Initial conditions:

$$\begin{align}x_{0}(0)&=1.0\end{align}$$

Parameter:

$$\begin{align}par_{0}&\subset~\left[ 1.0, 2.0\right]\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~1.0 \cdot e^{t \cdot \left[ -2.0, -1.0\right]}\end{align}$$

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=0.08670
c5: t_us=0.08630 , e_us=5.695770664152591e-02
c6: t_bd=10.000000 , e_bd=4.482702550411224e-05

DynIbex

arithmetic: Interval
method: 7
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 1

c4: t_c=0.20590
c5: t_us=0.20370 , e_us=5.695770664152591e-02
c6: t_bd=10.000000 , e_bd=4.482702550411224e-05

DynIbex

arithmetic: Interval
method: 9
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.25960
c5: t_us=0.25580 , e_us=6.290460029919123e-02
c6: t_bd=10.000000 , e_bd=8.206169500082517e-05

DynIbex

arithmetic: Interval
method: 11
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.30660
c5: t_us=0.30200 , e_us=6.701493257366245e-02
c6: t_bd=10.000000 , e_bd=1.085384149735879e-04

VNODE-LP

method: HOE
order: 10
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.00410
c5: t_us=0.00250 , e_us=0.0833902610573649
c6: t_bd=10 , e_bd=0.000123911067610013

VNODE-LP

method: HOE
order: 15
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.00810
c5: t_us=0.00490 , e_us=0.23729877513323
c6: t_bd=10 , e_bd=0.00358199790291205

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=0.00800 , e_us=1.45721352846516
c6: t_bd=10 , e_bd=1.02263860695824

VNODE-LP

method: HOE
order: 5
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.02680
c5: t_us=0.02170 , e_us=0.0572306556916891
c6: t_bd=10 , e_bd=4.59979981032021e-05

Generate graphics:

DynIbex VNODE-LP

WPD for Problem 9

IVP 70

Class: PILAU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.5, 1.5\right]\end{align}$$

Parameter:

$$\begin{align}par_{0}&=1.5\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~e^{- 1.5 \cdot t} \cdot \left[ 0.5, 1.5\right]\end{align}$$

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=0.04370
c5: t_us=0.04140 , e_us=1.102170577027550e-10
c6: t_bd=10.000000 , e_bd=7.270868557650610e-12

DynIbex

arithmetic: Interval
method: 7
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 1

c4: t_c=0.10740
c5: t_us=0.10230 , e_us=1.102170577027550e-10
c6: t_bd=10.000000 , e_bd=7.270868557650610e-12

DynIbex

arithmetic: Interval
method: 9
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.14110
c5: t_us=0.13560 , e_us=1.485310838765241e-04
c6: t_bd=10.000000 , e_bd=4.797183363840477e-08

DynIbex

arithmetic: Interval
method: 11
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.17210
c5: t_us=0.16450 , e_us=5.131253420245785e-04
c6: t_bd=8.841299 , e_bd=2.11047e-06

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=0.00230 , e_us=7.32747196252603e-15
c6: t_bd=10 , e_bd=6.99452025161931e-15

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=0.00440 , e_us=4.44089209850063e-16
c6: t_bd=10 , e_bd=8.34835672813838e-18

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=0.00700 , e_us=2.22044604925031e-16
c6: t_bd=10 , e_bd=1.13163601753175e-18

VNODE-LP

method: HOE
order: 5
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.02070
c5: t_us=0.01430 , e_us=2.47690756793872e-13
c6: t_bd=10 , e_bd=1.0647797747676e-13

Generate graphics:

DynIbex VNODE-LP

WPD for Problem 70

IVP 71

Class: PILAU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.5, 1.5\right]\end{align}$$

Parameter:

$$\begin{align}par_{0}&\subset~\left[ 1, 2\right]\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~e^{t \cdot \left[ -2, -1\right]} \cdot \left[ 0.5, 1.5\right]\end{align}$$

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=0.09230
c5: t_us=0.09200 , e_us=1.732309893023110e-01
c6: t_bd=10.000000 , e_bd=6.753607230577242e-05

DynIbex

arithmetic: Interval
method: 7
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 1

c4: t_c=0.17950
c5: t_us=0.17730 , e_us=1.732309893023110e-01
c6: t_bd=10.000000 , e_bd=6.753607230577242e-05

DynIbex

arithmetic: Interval
method: 9
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.23220
c5: t_us=0.22960 , e_us=1.831326305832948e-01
c6: t_bd=10.000000 , e_bd=1.204301817477188e-04

DynIbex

arithmetic: Interval
method: 11
abs. tolerance: 1e-12
initial stepsize: 1e-3
min. stepsize: 1e-5
monotonicity: 0

c4: t_c=0.28090
c5: t_us=0.27640 , e_us=1.899354087062128e-01
c6: t_bd=10.000000 , e_bd=1.584274985558571e-04

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=0.218373571074609
c6: t_bd=10 , e_bd=0.000179204709614807

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=0.00440 , e_us=0.433383092232264
c6: t_bd=10 , e_bd=0.00427159365063777

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=0.00710 , e_us=0.598418294299939
c6: t_bd=10 , e_bd=1.42792112995023

VNODE-LP

method: HOE
order: 5
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.02660
c5: t_us=0.02150 , e_us=0.173617250378609
c6: t_bd=10 , e_bd=6.91287503580817e-05

Generate graphics:

DynIbex VNODE-LP

WPD for Problem 71

IVP 81

Class: PILANU

Initial conditions:

$$\begin{align}x_{0}(0)&=-2.0\end{align}$$

Parameter:

$$\begin{align}par_{0}&=-0.5\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&=- 2.0 \cdot e^{0.5 \cdot t}\end{align}$$

[untested]

IVP 82

Class: PILAU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ -1.5, -0.5\right]\end{align}$$

Parameter:

$$\begin{align}par_{0}&\subset~\left[ -2.0, -1.0\right]\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~e^{t \cdot \left[ 1.0, 2.0\right]} \cdot \left[ -1.5, -0.5\right]\end{align}$$

[untested]

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

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A1 DETEST

Equations:

Description:

Keywords:

Plots:

Initial value problems:

IVP 1

Class: PILANU

Initial conditions:

Parameter:

Exact Solution*:

View test data:

Generate graphics:

IVP 2

Class: PILANU

Initial conditions:

Parameter:

Exact Solution*:

IVP 9

Class: PILAU

Initial conditions:

Parameter:

Exact Solution*:

View test data:

Generate graphics:

IVP 70

Class: PILAU

Initial conditions:

Parameter:

Exact Solution*:

View test data:

Generate graphics:

IVP 71

Class: PILAU

Initial conditions:

Parameter:

Exact Solution*:

View test data:

Generate graphics:

IVP 81

Class: PILANU

Initial conditions:

Parameter:

Exact Solution*:

IVP 82

Class: PILAU

Initial conditions:

Parameter:

Exact Solution*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*: