Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project
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Stability Optimization: a toy example<br />
As an example, consider the advection equation<br />
ut + ux = 0<br />
discretized in space by first-order upwind differencing with unit spatial<br />
mesh size<br />
U ′ i (t) = −(Ui(t) − Ui−1(t))<br />
with periodic boundary condition U0(t) = UN(t).<br />
8<br />
6<br />
4<br />
2<br />
0<br />
2<br />
4<br />
6<br />
8<br />
4 3 2 10 1<br />
D. Ketcheson (KAUST) 14 / 36