Questions tagged [derivative]

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3 votes
2 answers
1k views

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 $$ f(x) = \exp(-10(x-1)^2) ,\, \, x \in [0,2] $$ ...
NNN's user avatar
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4 votes
1 answer
269 views

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 ...
Nikola Ristic's user avatar
4 votes
1 answer
157 views

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 ...
Glenn Davis's user avatar
1 vote
2 answers
2k views

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 ...
Nikola Ristic's user avatar
3 votes
1 answer
270 views

Finite difference problem

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 ...
Kaneki Ken's user avatar
1 vote
1 answer
83 views

derivative matrix and the Dirac delta distribution

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 ...
NNN's user avatar
  • 670