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Unstable ODEby muzialis
Tags: unstable 
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#1
Nov2912, 09:53 AM

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 wellposedness, 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 


#2
Nov2912, 01:26 PM

HW Helper
P: 1,391

In this way you can construct a piecewise analytic solution for some simple parameter choices which you can test against your numerical solution. 


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