# Unstable ODE

by muzialis
Tags: unstable
 P: 152 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
 Quote by muzialis 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