Simple Stiff 1

Equations:

$$\begin{align}\dot{x}_{0}&=- 80.6 \cdot x_{0} + 119.4 \cdot x_{1}\\\dot{x}_{1}&=79.6 \cdot x_{0} - 120.4 \cdot x_{1}\end{align}$$

Description:

A simple linear system of equations which is stiff for certain initial conditions.

Keywords:

stiff

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Plots:

C5 WPD

Initial value problems:

130 (PIILANU)
131 (PIILAU)

IVP 130

Class: PIILANU

Initial conditions:

$$\begin{align}x_{0}(0)&=0.0\\x_{1}(0)&=5.0\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&=- 3.0 \cdot e^{- 200.0 \cdot t} + 3.0 \cdot e^{- t}\\x_{1}(t)&=3.0 \cdot e^{- 200.0 \cdot t} + 2.0 \cdot e^{- t}\end{align}$$

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=0.03620
c5: t_us=0.03490 , e_us=3.560485239972877e-13
c6: t_bd=10.000000 , e_bd=7.668101180066667e-15

VNODE-LP

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

c4: t_c=0.05430
c5: t_us=0.05180 , e_us=1.133537708142285e-13
c6: t_bd=10.000000 , e_bd=3.908277781267122e-16

VNODE-LP

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

c4: t_c=0.06850
c5: t_us=0.06470 , e_us=8.371081605673680e-14
c6: t_bd=10.000000 , e_bd=1.148170100662149e-16

VNODE-LP

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

c4: t_c=999
c5: t_us=999 , e_us=999
c6: t_bd=1e-308 , e_bd=1e-308

Generate graphics:

VNODE-LP

WPD for Problem 130

IVP 131

Class: PIILAU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.0, 1.0\right]\\x_{1}(0)&\subset~\left[ 4.55, 5.05\right]\end{align}$$

Exact Solution^*:

$$\begin{align}x_{0}(t)&\subset~e^{- 200.0 \cdot t} \cdot \left[ -3.03, -2.33\right] + e^{- t} \cdot \left[ 2.13, 3.03\right]\\x_{1}(t)&\subset~e^{- 200.0 \cdot t} \cdot \left[ 2.33, 3.03\right] + e^{- t} \cdot \left[ 1.42, 2.02\right]\end{align}$$