C4 DETEST

Equations:

$$\begin{align}\dot{x}_{0}&=- 2.0 \cdot x_{0} + x_{1}\\\dot{x}_{1}&=x_{0} - 2.0 \cdot x_{1} + x_{2}\\\dot{x}_{2}&=x_{1} - 2.0 \cdot x_{2} + x_{3}\\\dot{x}_{3}&=x_{2} - 2.0 \cdot x_{3} + x_{4}\\\dot{x}_{4}&=x_{3} - 2.0 \cdot x_{4} + x_{5}\\\dot{x}_{5}&=x_{4} - 2.0 \cdot x_{5} + x_{6}\\\dot{x}_{6}&=x_{5} - 2.0 \cdot x_{6} + x_{7}\\\dot{x}_{7}&=x_{6} - 2.0 \cdot x_{7} + x_{8}\\\dot{x}_{8}&=x_{7} - 2.0 \cdot x_{8} + x_{9}\\\dot{x}_{9}&=x_{10} + x_{8} - 2.0 \cdot x_{9}\\\dot{x}_{10}&=- 2.0 \cdot x_{10} + x_{11} + x_{9}\\\dot{x}_{11}&=x_{10} - 2.0 \cdot x_{11} + x_{12}\\\dot{x}_{12}&=x_{11} - 2.0 \cdot x_{12} + x_{13}\\\dot{x}_{13}&=x_{12} - 2.0 \cdot x_{13} + x_{14}\\\dot{x}_{14}&=x_{13} - 2.0 \cdot x_{14} + x_{15}\\\dot{x}_{15}&=x_{14} - 2.0 \cdot x_{15} + x_{16}\\\dot{x}_{16}&=x_{15} - 2.0 \cdot x_{16} + x_{17}\\\dot{x}_{17}&=x_{16} - 2.0 \cdot x_{17} + x_{18}\\\dot{x}_{18}&=x_{17} - 2.0 \cdot x_{18} + x_{19}\\\dot{x}_{19}&=x_{18} - 2.0 \cdot x_{19} + x_{20}\\\dot{x}_{20}&=x_{19} - 2.0 \cdot x_{20} + x_{21}\\\dot{x}_{21}&=x_{20} - 2.0 \cdot x_{21} + x_{22}\\\dot{x}_{22}&=x_{21} - 2.0 \cdot x_{22} + x_{23}\\\dot{x}_{23}&=x_{22} - 2.0 \cdot x_{23} + x_{24}\\\dot{x}_{24}&=x_{23} - 2.0 \cdot x_{24} + x_{25}\\\dot{x}_{25}&=x_{24} - 2.0 \cdot x_{25} + x_{26}\\\dot{x}_{26}&=x_{25} - 2.0 \cdot x_{26} + x_{27}\\\dot{x}_{27}&=x_{26} - 2.0 \cdot x_{27} + x_{28}\\\dot{x}_{28}&=x_{27} - 2.0 \cdot x_{28} + x_{29}\\\dot{x}_{29}&=x_{28} - 2.0 \cdot x_{29} + x_{30}\\\dot{x}_{30}&=x_{29} - 2.0 \cdot x_{30} + x_{31}\\\dot{x}_{31}&=x_{30} - 2.0 \cdot x_{31} + x_{32}\\\dot{x}_{32}&=x_{31} - 2.0 \cdot x_{32} + x_{33}\\\dot{x}_{33}&=x_{32} - 2.0 \cdot x_{33} + x_{34}\\\dot{x}_{34}&=x_{33} - 2.0 \cdot x_{34} + x_{35}\\\dot{x}_{35}&=x_{34} - 2.0 \cdot x_{35} + x_{36}\\\dot{x}_{36}&=x_{35} - 2.0 \cdot x_{36} + x_{37}\\\dot{x}_{37}&=x_{36} - 2.0 \cdot x_{37} + x_{38}\\\dot{x}_{38}&=x_{37} - 2.0 \cdot x_{38} + x_{39}\\\dot{x}_{39}&=x_{38} - 2.0 \cdot x_{39} + x_{40}\\\dot{x}_{40}&=x_{39} - 2.0 \cdot x_{40} + x_{41}\\\dot{x}_{41}&=x_{40} - 2.0 \cdot x_{41} + x_{42}\\\dot{x}_{42}&=x_{41} - 2.0 \cdot x_{42} + x_{43}\\\dot{x}_{43}&=x_{42} - 2.0 \cdot x_{43} + x_{44}\\\dot{x}_{44}&=x_{43} - 2.0 \cdot x_{44} + x_{45}\\\dot{x}_{45}&=x_{44} - 2.0 \cdot x_{45} + x_{46}\\\dot{x}_{46}&=x_{45} - 2.0 \cdot x_{46} + x_{47}\\\dot{x}_{47}&=x_{46} - 2.0 \cdot x_{47} + x_{48}\\\dot{x}_{48}&=x_{47} - 2.0 \cdot x_{48} + x_{49}\\\dot{x}_{49}&=x_{48} - 2.0 \cdot x_{49} + x_{50}\\\dot{x}_{50}&=x_{49} - 2.0 \cdot x_{50}\end{align}$$

Description:

Derived from a parabolic partial differential equation; n=51.
Link to DETEST description

Keywords:

min test set

Download file

Plots:

C5 WPD

IVP 15

Class: PILCU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ 0.5, 1.5\right]\\x_{1}(0)&=0.0\\x_{2}(0)&=0.0\\x_{3}(0)&=0.0\\x_{4}(0)&=0.0\\x_{5}(0)&=0.0\\x_{6}(0)&=0.0\\x_{7}(0)&=0.0\\x_{8}(0)&=0.0\\x_{9}(0)&=0.0\\x_{10}(0)&=0.0\\x_{11}(0)&=0.0\\x_{12}(0)&=0.0\\x_{13}(0)&=0.0\\x_{14}(0)&=0.0\\x_{15}(0)&=0.0\\x_{16}(0)&=0.0\\x_{17}(0)&=0.0\\x_{18}(0)&=0.0\\x_{19}(0)&=0.0\\x_{20}(0)&=0.0\\x_{21}(0)&=0.0\\x_{22}(0)&=0.0\\x_{23}(0)&=0.0\\x_{24}(0)&=0.0\\x_{25}(0)&=0.0\\x_{26}(0)&=0.0\\x_{27}(0)&=0.0\\x_{28}(0)&=0.0\\x_{29}(0)&=0.0\\x_{30}(0)&=0.0\\x_{31}(0)&=0.0\\x_{32}(0)&=0.0\\x_{33}(0)&=0.0\\x_{34}(0)&=0.0\\x_{35}(0)&=0.0\\x_{36}(0)&=0.0\\x_{37}(0)&=0.0\\x_{38}(0)&=0.0\\x_{39}(0)&=0.0\\x_{40}(0)&=0.0\\x_{41}(0)&=0.0\\x_{42}(0)&=0.0\\x_{43}(0)&=0.0\\x_{44}(0)&=0.0\\x_{45}(0)&=0.0\\x_{46}(0)&=0.0\\x_{47}(0)&=0.0\\x_{48}(0)&=0.0\\x_{49}(0)&=0.0\\x_{50}(0)&=0.0\end{align}$$

Exact Solution^*:

No exact solution provided.

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=1.92840
c5: t_us=1.92580 , e_us=1.066258973703882e-26
c6: t_bd=10.000000 , e_bd=1.278072419707443e-15

VNODE-LP

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

c4: t_c=2.46110
c5: t_us=2.45620 , e_us=4.418905439418671e-28
c6: t_bd=10.000000 , e_bd=8.431670728423203e-17

VNODE-LP

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

c4: t_c=2.73870
c5: t_us=2.73140 , e_us=2.661504883489686e-30
c6: t_bd=10.000000 , e_bd=2.069515426279561e-17

VNODE-LP

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

c4: t_c=122.56670
c5: t_us=122.55580 , e_us=4.198399203513196e-27
c6: t_bd=10.000000 , e_bd=3.185639049734532e-14

Generate graphics:

VNODE-LP

WPD for Problem 15

IVP 84

Class: PILCNU

Initial conditions:

$$\begin{align}x_{0}(0)&=1.0\\x_{1}(0)&=0.0\\x_{2}(0)&=0.0\\x_{3}(0)&=0.0\\x_{4}(0)&=0.0\\x_{5}(0)&=0.0\\x_{6}(0)&=0.0\\x_{7}(0)&=0.0\\x_{8}(0)&=0.0\\x_{9}(0)&=0.0\\x_{10}(0)&=0.0\\x_{11}(0)&=0.0\\x_{12}(0)&=0.0\\x_{13}(0)&=0.0\\x_{14}(0)&=0.0\\x_{15}(0)&=0.0\\x_{16}(0)&=0.0\\x_{17}(0)&=0.0\\x_{18}(0)&=0.0\\x_{19}(0)&=0.0\\x_{20}(0)&=0.0\\x_{21}(0)&=0.0\\x_{22}(0)&=0.0\\x_{23}(0)&=0.0\\x_{24}(0)&=0.0\\x_{25}(0)&=0.0\\x_{26}(0)&=0.0\\x_{27}(0)&=0.0\\x_{28}(0)&=0.0\\x_{29}(0)&=0.0\\x_{30}(0)&=0.0\\x_{31}(0)&=0.0\\x_{32}(0)&=0.0\\x_{33}(0)&=0.0\\x_{34}(0)&=0.0\\x_{35}(0)&=0.0\\x_{36}(0)&=0.0\\x_{37}(0)&=0.0\\x_{38}(0)&=0.0\\x_{39}(0)&=0.0\\x_{40}(0)&=0.0\\x_{41}(0)&=0.0\\x_{42}(0)&=0.0\\x_{43}(0)&=0.0\\x_{44}(0)&=0.0\\x_{45}(0)&=0.0\\x_{46}(0)&=0.0\\x_{47}(0)&=0.0\\x_{48}(0)&=0.0\\x_{49}(0)&=0.0\\x_{50}(0)&=0.0\end{align}$$