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I have problem with determining the stability region for forward Euler method with equation:

$$ y' = -100y + 100 \cos t - \sin t \quad t \in[0, \pi], \quad y(0)= 1$$

Forward Euler method is defined as:

$$ y_{n+1} = y_{n} + hf(t_n, y_n)$$

How to find stability region in that case? I think that it's the same as for equation $y' = -100y$, which is $h<0.02$, but that's just my guess (confirmed by the graphical plots) and I don't know how to check it.

joel_embiid
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  • Well, what's the procedure for determining stability? – user7530 Jan 09 '18 at 21:19
  • In case $y' = -ky$ we know that forward Euler method is $y_{n+1} = (1-kh)y_n$, so $y_{n+1} = (1-kh)^n ,y_0$ and then we check when (for which $k$) $(1-kh)^n$ with $n \to \infty$ converges to 0 like the solution of that equation. I don't know how to do that in my case (the solution is $y=cos(t)$) – joel_embiid Jan 09 '18 at 21:44

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