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I am solving numerically the ODE

$$ \dot{y} = min \, (y, A) + B\, sin(t)$$ , A,B being constant.

I obtain a very "wiggled" solution which is very fine to me actually, as it echoes the problem I am studying.

However, as the numerical solution scheme is quite "rudimentary" I am wondering if I am getting an accurate answer.

In this respect I am wondering if somebody could point me towards a suitable theory for ODE to study their well-posedness, continuity with respect to inital data, stability.

I am no expert, but I understand the problems one would encounter if trying to solve the heat equation with negative conductvity!

The ODE, in the regime $$ y(t) < A$$ is of they type $$ \dot{y} = y + f(t)$$ which is prone to diverging exponentially.

I am trying to understand if the solution I find is meanigful or just "computer noise".

Thanks

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# Unstable ODE

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