pymordemos.unstable_heat

Module Contents

pymordemos.unstable_heat.main(l: float = Argument(50, help='Parameter for instability.'), r: int = Argument(10, help='Order of the ROMs.'))

1D unstable heat equation demo.

Discretization of the PDE:

\[\begin{split}\begin{align} \partial_t T(\xi, t) &= \partial_{\xi \xi} T(\xi, t) + \lambda T(\xi, t), & 0 < \xi < 1,\ t > 0, \\ -\partial_\xi T(0, t) & = -T(0, t) + u(t), & t > 0, \\ \partial_\xi T(1, t) & = -T(1, t), & t > 0, \\ y(t) & = T(1, t), & t > 0 \end{align}\end{split}\]