Polynomial Inequalities and Optimal Stability of Numerical Integrators

Luke Shaw

A numerical integrator for $\dot{x}=f(x)$ is called \emph{stable} if, when applied to the 1D Dahlquist test equation $\dot{x}=\hat{I}»x,\hat{I}»\in \mathbb{C}$ with fixed timestep $h>0$, the nu…