Understanding how Matlab approximations work
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Dear all,
I have what may be a naive question about how Matlab truly works. I have an ODE whose solution lies on the unit sphere. One of the equilibrium points is (1,0,0). When I look for the equilibrium points using numerical methods, Matlab tells me that the equilibrium point is
1.000000000000000
0
0.000000000000000
When I then try to solve the equation, after some time, the solution of the equation leaves the equilibrium and starts to go around the sphere. But if before solving the equation I specify to Matlab to start from the point
1
0
0
then nothing happens (which is rather normal since the point is an equilibrium one, even if unstable). My question is therefore, why does the solution leave the equilibrium when the starting point is
1.000000000000000
0
0.000000000000000
To me, this was the exact same as
1
0
0
since I thought Matlab did not use more than 16 digits. But I am obviously wrong since the solutions are not the same... Is Matlab hiding me some numerical approximations somewhere?
Thank you very much
0 Comments
Answers (1)
per isakson
on 9 Apr 2013
Try
format hex
6 Comments
per isakson
on 9 Apr 2013
Edited: per isakson
on 9 Apr 2013
Communication is tricky. I tried to say that the two sets of inputs are indentical. (I added the word "inputs" in my previous comment.)
>> format hex
>> 1,0,0
ans =
3ff0000000000000
ans =
0000000000000000
ans =
0000000000000000
>> 1.0000, 0.0000, 0.0000
ans =
3ff0000000000000
ans =
0000000000000000
ans =
0000000000000000
>>
Still the two outputs differ.
Did you try to step through the code?
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