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I have the task to compute the Fourier transform of the product in matlab:

$$ \left( \frac{\partial u(t, x)}{\partial x} \right)^2 \left( \frac{\partial^2 u(t, x)}{\partial x^2 } \right)$$

I was trying to avoid the use of convolution since whenever I tried using that, numerical errors affect the result. Thus, I was trying to find the better way to not use the matlab convolution function.

As a start, I re-express the above function in the form

$$\frac{1}{3}\frac{\partial } {\partial x} \bigg[\left(\frac{\partial u(t, x)}{\partial x} \right)^3 \bigg] $$ equalling the above term.

Yet, I got stuck with the derivative in the composition. Any idea how to continue or better way to compute the derivative in matlab efficiently?

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  • $\begingroup$ Do you have $u(t,x)$ in closed form or is it a 2-dim array with discrete data points? $\endgroup$
    – gpmath
    Commented Jun 20 at 14:47
  • $\begingroup$ It is actually 2-dim array with discrete data points. $\endgroup$
    – unknown
    Commented Jun 21 at 13:23
  • $\begingroup$ Here you'll find a MATLAB example how to get the derivatives: MSE_Q4935016 $\endgroup$
    – gpmath
    Commented Jun 21 at 14:50

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