Harmonic Oscillator 1

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Harmonic Oscillator 1

Equations:

$$\begin{align}\dot{x}_{0}&=x_{1}\\\dot{x}_{1}&=- 4.0 \cdot x_{0}\end{align}$$

Description:

no description available

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Plots:

C5 WPD

Initial value problems:

16 (PILANU)
17 (PILAU)

IVP 16

Class: PILANU

Initial conditions:

$$\begin{align}x_{0}(0)&=1.0\\x_{1}(0)&=1.0\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&=0.5 \cdot \sin {2.0 \cdot t} + 1.0 \cdot \cos {2.0 \cdot t}\\x_{1}(t)&=- 2.0 \cdot \sin {2.0 \cdot t} + 1.0 \cdot \cos {2.0 \cdot t}\end{align}$$

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=0.00410
c5: t_us=0.00330 , e_us=1.065814103640150e-14
c6: t_bd=10.000000 , e_bd=1.663114090888484e-13

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=0.00700 , e_us=1e-308
c6: t_bd=10.000000 , e_bd=2.087219286295294e-14

VNODE-LP

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

c4: t_c=0.01210
c5: t_us=0.00970 , e_us=1e-308
c6: t_bd=10.000000 , e_bd=6.816769371198461e-14

VNODE-LP

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

c4: t_c=0.03960
c5: t_us=0.03450 , e_us=1.046274178406748e-12
c6: t_bd=10.000000 , e_bd=9.994449712280584e-12

Generate graphics:

VNODE-LP

WPD for Problem 16

IVP 17

Class: PILAU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.5, 1.0\right]\\x_{1}(0)&=1.0\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~0.5 \cdot \sin {2.0 \cdot t} + \cos {2.0 \cdot t} \cdot \left[ 0.5, 1.0\right]\\x_{1}(t)&\subset~\sin {2.0 \cdot t} \cdot \left[ -2.0, -1.0\right] + 1.0 \cdot \cos {2.0 \cdot t}\end{align}$$