unstable_heatΒΆ
pymor-demo unstable_heat [ARGS]
1D unstable heat equation demo.
Discretization of the PDE:
\[\begin{split}\begin{align}
\partial_t T(\xi, t) &= \partial_{\xi \xi} T(\xi, t) + \lambda T(\xi, t),
& 0 < \xi < 1,\ t > 0, \\
-\partial_\xi T(0, t) & = -T(0, t) + u(t),
& t > 0, \\
\partial_\xi T(1, t) & = -T(1, t),
& t > 0, \\
y(t) & = T(1, t),
& t > 0
\end{align}\end{split}\]
Parameters:
L, --lParameter for instability. [Default:
50.0]R, --rOrder of the ROMs. [Default:
10]