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Integral equations in Wolfram Language

Yaj Bhattacharya
Posted 11 years ago

Hello, Could someone point me to approaches at solving the following type of integral equation in Mathematica (p and q are variables, " f " is a function of either p, or q , and \omega is a function of p, q or both p and q, as well as \mu and m. A, \mu and m are constants): enter image description here
POSTED BY: Yaj Bhattacharya
8 Replies
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Thank you Sean and Henrick. I too am not a mathematician, and this is my first encounter with an Integral equation! There was no expectation or intent to punch in this sort of an equation in a Notebook and press "Shift-Enter" for a solution. I don't want to convert it to a differential equation.
POSTED BY: Yaj Bhattacharya

Hennrik, On a completely separate note, how do you typset your post to include such nice math symbols?
POSTED BY: Yaj Bhattacharya

Dear Yaj,

this typesetting is a nice feature, isn't it! To use it one just hast to apply the LaTeX syntax, see How to Post ...

Concerning integral equations: I find very helpful

Andrei D. Polyanin, Alexander V. Manzhirov; Handbook of Integral Equations

Henrik
POSTED BY: Henrik Schachner

Hi Yaj,

I hope my remark is not too silly (because unfortunately I am not a mathematician): Are you sure that your equation has a solution anyway? The general form is:

$f(q) = \int f(p) K(q,p)\mbox{d}p$

and this is true for $K(q,p) = \delta(p-q)$, but in your case $K$ is not the Dirac-Deltafunction ...

Henrik
POSTED BY: Henrik Schachner
POSTED BY: Henrik Schachner

Don't use special characters. Just use regular english keyboard characters.

Other than that, I would see if you can work out how to turn this into a differential equation on a chalkboard.
POSTED BY: Sean Clarke

When I try to post the code, I get this

[q] (2 \[Omega][q, \[Mu]] - A) = \[Pi] \[Integral](
   f[p] \[DifferentialD]p)/(\[Omega][
     q, \[Mu]] (\[Omega][p - q, m])^2 \[Omega][p, \[Mu]])
POSTED BY: Yaj Bhattacharya
POSTED BY: Sean Clarke
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