ssp_rk3
intsharp/solvers/euler_dg_1d.py
SSP-RK3 (DG Internal)
This strong-stability-preserving third-order Runge-Kutta scheme is used internally by the 1D DG Euler solver.
\[
\begin{aligned}
\mathbf{U}^{(1)} &= \mathbf{U}^n + \Delta t\,\mathcal{L}\!\left(\mathbf{U}^n\right),\\
\mathbf{U}^{(2)} &= \tfrac{3}{4}\mathbf{U}^n + \tfrac{1}{4}\left(\mathbf{U}^{(1)} + \Delta t\,\mathcal{L}\!\left(\mathbf{U}^{(1)}\right)\right),\\
\mathbf{U}^{n+1} &= \tfrac{1}{3}\mathbf{U}^n + \tfrac{2}{3}\left(\mathbf{U}^{(2)} + \Delta t\,\mathcal{L}\!\left(\mathbf{U}^{(2)}\right)\right).
\end{aligned}
\]
For DG, this is coupled with limiter/positivity conditioning between stages. This is not currently selected through timestepper.type; it is part of the DG step implementation.