Convergence of a numerical method
= Convergence of a numerical method
{title2=$\max_{t_n\leq T}\|y_n-y(t_n)\|\to0$}
For an <initial value problem>, convergence means that the largest <global error> on each fixed finite time interval tends to zero as the step size tends to zero and the starting errors vanish. For <linear multistep methods>, the <Dahlquist equivalence theorem> separates this requirement into <consistency of a numerical method> and <zero-stability>.