E4 DETEST

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Equations:

$$\begin{align}\dot{x}_{0}&=x_{1}\\\dot{x}_{1}&=0.032 - 0.4 \cdot x_{1}^{2}\end{align}$$

Description:

Derived from the equation of motion for a falling body.
Link to DETEST description

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Plots:

C5 WPD

Initial value problems:

66 (PINLBNU)
67 (PINLBU)

IVP 66

Class: PINLBNU

Initial conditions:

$$\begin{align}x_{0}(0)&=30.0\\x_{1}(0)&=0.0\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&=2.5 \cdot \log{\left(\cosh {0.113137084989848 \cdot t} \right)} + 30.0\\x_{1}(t)&=0.282842712474619 - \frac{0.565685424949238}{1.0 \cdot e^{0.226274169979695 \cdot t} + 1}\end{align}$$

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=0.00320 , e_us=1.190020304520090e-14
c6: t_bd=10.000000 , e_bd=4.782008122816706e-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=0.00480 , e_us=1.387778780781446e-17
c6: t_bd=10.000000 , e_bd=2.532307696867520e-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=0.00760 , e_us=2.775557561562891e-17
c6: t_bd=10.000000 , e_bd=1.369876434509365e-12

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=0.01190 , e_us=1.752070710736575e-14
c6: t_bd=10.000000 , e_bd=4.486688798266414e-13

Generate graphics:

VNODE-LP

WPD for Problem 66

IVP 67

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 29.5, 30.5\right]\\x_{1}(0)&=0.0\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~2.5 \cdot \log{\left(\cosh {0.113137084989848 \cdot t} \right)} + \left[ 29.5, 30.5\right]\\x_{1}(t)&=0.282842712474619 - \frac{0.565685424949238}{1.0 \cdot e^{0.226274169979695 \cdot t} + 1}\end{align}$$