Stability of a Method

A method $T$ is stable if, for a stable ODE, two slightly different initial conditions $y_A(0)$ and $y_B(0)=y_A(0)+ϵ$ produce solutions $y_{T,A}(t)$ and $y_{T,B}(t)$ whose difference stays bounded - i.e., there exists $M(ϵ)$ such that $|y_{T,A}(t)-y_{T,B}(t)|<M$ for all $t>0$.