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, --l

Parameter for instability. [Default: 50.0]

R, --r

Order of the ROMs. [Default: 10]