Convergence of numerical ODE solvers and Lyapunov's theory of stability

Divakar Viswanath

For the ordinary differential equation (ODE) $\dot{x}(t)=f(t,x)$, $x(0)=x_0$, $t\ge 0$, $x\in R^d$, assume $f$ to be at least continuous in $t$ and locally Lipshitz in $x$, an…