# Questions tagged [derivative]

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### compute accurate derivatives using FFT

I'm trying to learn how to compute accurate derivatives using the FFT. In the code at the end of this question I'm trying to compute derivatives of $$f(x) = \exp(-10(x-1)^2) ,\, \, x \in [0,2]$$ ...
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### How to evaluate the points near/at the boundary when using Richardson extrapolation for improved accuracy of a derivative

If we want to improve the accuracy of our numerical estimation of a derivative, we can use Richardson extrapolation. The method is very beneficial when using a centered difference scheme and the ...
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### Is there a software package that can compute the 1-dimensional preimage of a point?

I have a smooth function $F: \mathbb{R}^n \to \mathbb{R}^{n-1}$ and points $x_0, y_0$ with $F(x_0) = y_0$. For theoretical reasons, I know that $y_0$ is a regular value of $F$, which means that the ...
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### When can I use finite differences for differentiation?

Finite differences are usually used to integrate ODE's and PDE's. However, sometimes they can be used for differentiation which I illustrated simply by using the Matlab code below to differentiate the ...
I have a problem to resolve with the Finite Difference method in $[a,b]$: $$-\frac{d}{dx}(\alpha(x)\frac{du}{dx})= g(x),$$ with $\alpha(x) \in L^{\infty}$ continuous in $]a,c[$ and $]c,b[$ and ...
For a project I'm working on, I was working with the following equation $$w(x) = \int k(x,y)v(y)dy$$ I noticed that if I choose $$k(x,y) = -\delta'(x-y)$$ Then we probably get (I haven't touched ...