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Let $y'(t)=f(t,y(t))$ and $y(0)=y_0$
The backward euler method together with the center rule is given by:
$y(t_k)=hk$ where $h\in (0,\frac{1}{K})$ is the step size.
Recursion: $y_k=y_{k-1}+hf(t_{k-1}+\frac{h}{2},\mu_{k-1})$ where $\mu_{k-1}=y_{k-1}+\frac{h}{2}f(t_{k-1},y_{k-1})$
Question: I want to use the method now for $y'(t)=\lambda y(t), t>0$ and $y(0)=y_0$ to evaluate for which $\lambda$ the sequence $(y_k)_{k\in\mathbb N}$ converges to $0$
I tried to evaluate some $y_k$ but I couldn' tsee anything.