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Inconsistent results for second derivative of inverse fourier transform

Posted 11 years ago
Hi,

I am trying to get the green's function of a toy diffusion equation with Mathematica 9






Then solve by inverse fourier transform
In[3]:= u[x_, t_] := InverseFourierTransform[U[k, t], k, x]
D[u[x, t], {x, 2}] 
D[D[u[x, t], x], x] 

Out[4]= 0 
Out[5]= InverseFourierTransform[-k^2 U[k, t], k, x]
But can someone tell me why Out[4] and Out[5] are different? Thanks for your kindness.
POSTED BY: Guo Zhou
3 Replies
Hi Guo, 

Sorry there is this bug in the system, unfortunately I don't have the power/resources to fix it. For now, you have to find another way to solve your problem.
POSTED BY: Sander Huisman
Posted 11 years ago
Hi Huisman,
Thanks for your reply. I've  just contacted Wolfram technical support, and it should be a bug
Hello Guo Zhou,
Thank you for brining this issue to our attention.
I recreated the behavior you described and I found the issue can be seen when only examining the first derivative. Please see the attached notebook for details. I have filed a note with the appropriate members of our development team regardng this.
We are always interested in improving Mathematica and I want to thank you again for taking the time to contact us about this issue. If you have any further questions, or if you find further issues, please feel free to contact us again.

attached notebook
 Simplifying issue.
 Immediately below is what you found:
 u[x_, t_] := InverseFourierTransform[U[k, t], k, x]
 D[u[x, t], {x, 2}]
 0
 D[D[u[x, t], x], x]
 InverseFourierTransform[-k^2 U[k, t], k, x]
 However, the issue becomes more clear when we see that the first derivative is being handled differently:
 D[u[x, t], x]
InverseFourierTransform[-I k U[k, t], k, x]
D[u[x, t], {x, 1}]
0
POSTED BY: Guo Zhou
Hi Guo,

Indeed this is strange, your second command in[4] should do the same I think as In[5].  

Also:
D[u[x, t], {x, 2}] 
D[u[x, t], x,x] 
give different answers, strange...
POSTED BY: Sander Huisman
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