E2 DETEST

Equations:

$$\begin{align}\dot{x}_{0}&=x_{1}\\\dot{x}_{1}&=par_{0} \cdot x_{1} \cdot \left(1.0 - x_{0}^{2}\right) - x_{0}\end{align}$$

Description:

Van der Pol oscillator. A non-conservative oscillator with non-linear damping; stiff for large par0.
Link to DETEST description

Keywords:

chaotic

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IVP 76

Class: PINLBNU

Initial conditions:

$$\begin{align}x_{0}(0)&=2.0\\x_{1}(0)&=0.0\end{align}$$

Parameter:

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

Exact Solution^*:

No exact solution provided.

[untested]

IVP 109

Class: PINLBNU

Initial conditions:

$$\begin{align}x_{0}(0)&=2.0\\x_{1}(0)&=0.0\end{align}$$

Parameter:

$$\begin{align}par_{0}&=2.0\end{align}$$

Exact Solution^*:

No exact solution provided.

[untested]

IVP 110

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 1.37, 1.43\right]\\x_{1}(0)&=2.25\end{align}$$

Parameter:

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

Exact Solution^*:

No exact solution provided.

[untested]

IVP 111

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 1.1, 1.7\right]\\x_{1}(0)&=2.25\end{align}$$

Parameter:

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

Exact Solution^*:

No exact solution provided.

[untested]

IVP 112

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.8, 2.0\right]\\x_{1}(0)&=2.25\end{align}$$

Parameter:

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

Exact Solution^*:

No exact solution provided.

[untested]

IVP 113

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ -0.1, 2.9\right]\\x_{1}(0)&=2.25\end{align}$$

Parameter:

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

Exact Solution^*:

No exact solution provided.

[untested]

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

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E2 DETEST

Equations:

Description:

Keywords:

Initial value problems:

IVP 76

Class: PINLBNU

Initial conditions:

Parameter:

Exact Solution*:

IVP 109

Class: PINLBNU

Initial conditions:

Parameter:

Exact Solution*:

IVP 110

Class: PINLBU

Initial conditions:

Parameter:

Exact Solution*:

IVP 111

Class: PINLBU

Initial conditions:

Parameter:

Exact Solution*:

IVP 112

Class: PINLBU

Initial conditions:

Parameter:

Exact Solution*:

IVP 113

Class: PINLBU

Initial conditions:

Parameter:

Exact Solution*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*:

Exact Solution^*: