- #1
muzialis
- 166
- 1
Hello there,
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
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