A4 DETEST

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Equations:

$$\begin{align}\dot{x}_{0}&=0.0125 \cdot x_{0} \cdot \left(20.0 - x_{0}\right)\end{align}$$

IVP 34

Class: PINLANU

Initial conditions:

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

Exact Solution^*:

$$\begin{align}x_{0}(t)&=\frac{20.0}{1.0 + 19.0 \cdot e^{- 0.25 \cdot t}}\end{align}$$

View test data:

Solver
Settings
Results

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=6.661338147750939e-16
c6: t_bd=10.000000 , e_bd=8.908429549592256e-13

VNODE-LP

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

c4: t_c=0.00780
c5: t_us=0.00550 , e_us=8.881784197001252e-16
c6: t_bd=10.000000 , e_bd=1.592503906522325e-12

VNODE-LP

method: HOE
order: 20
abs. tolerance: 1e-12
rel. tolerance: 1e-12
min. stepsize: 1e-05

c4: t_c=0.01180
c5: t_us=0.00770 , e_us=6.661338147750939e-16
c6: t_bd=10.000000 , e_bd=1.349143019524490e-12

VNODE-LP

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

c4: t_c=0.01670
c5: t_us=0.01270 , e_us=4.907185768843192e-14
c6: t_bd=10.000000 , e_bd=3.923972258235153e-12

Generate graphics:

VNODE-LP

WPD for Problem 34

IVP 35

Class: PINLAU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.5, 1.25\right]\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~\frac{20.0}{1.0 + e^{- 0.25 \cdot t} \cdot \left[ 15.0, 39.0\right]}\end{align}$$

View test data:

Solver
Settings
Results

VNODE-LP

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

c4: t_c=0.00390
c5: t_us=0.00240 , e_us=1.053412144655153e-02
c6: t_bd=10.000000 , e_bd=1.731698409268254e+00

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=0.00560 , e_us=1.010373158413569e-02
c6: t_bd=10.000000 , e_bd=2.052835353056887e+00

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=0.00800 , e_us=1.010369787700460e-02
c6: t_bd=10.000000 , e_bd=2.570030180096756e+00

VNODE-LP

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

c4: t_c=0.01690
c5: t_us=0.01100 , e_us=9.983561780645855e-03
c6: t_bd=10.000000 , e_bd=1.534394151505292e+00

Generate graphics:

VNODE-LP

WPD for Problem 35

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

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A4 DETEST

Equations:

Description:

Plots:

Initial value problems:

IVP 34

Class: PINLANU

Initial conditions:

Exact Solution*:

View test data:

Generate graphics:

IVP 35

Class: PINLAU

Initial conditions:

Exact Solution*:

View test data:

Generate graphics:

Exact Solution^*:

Exact Solution^*: