Discrete Gronwall inequality
= Discrete Gronwall inequality
If nonnegative quantities satisfy
$$
e_{n+1}\leq(1+hL)e_n+h b_n,
$$
then iteration gives
$$
e_n\leq(1+hL)^ne_0
+h\sum_{j=0}^{n-1}(1+hL)^{n-1-j}b_j.
$$
For $nh\leq T$, the growth factor is bounded by $e^{LT}$.