Forward Euler

Definition

$$y_{k+1}=y_k+\Delta tf(t_k,y_k)$$

when it’s linear, we can say

$$y_{k+1}=y_k+\Delta t\lambda y_k=y_k(1+\Delta t\lambda )$$

Stability

It’s stable only if all $\lambda$: $|1+h{\lambda }_i|\le 1$