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):
The first step in most cases is to write out the equation in Wolfram Language Code.
That said, there isn’t a way to just simply solve an integral equation. Can it be expressed as a differential equation of some kind?
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]])
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.
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
Ok, here comes a final note:
If the above equation is discretized, giving:
f(q_m) = \sum_n f(p_n) K(q_m, p_n)
one can see that f(q) needs to be an eigenvector for the matrix K with the eigenvalue 1. So maybe there are solutions. This actually could be explored with Mathematica. (This is always true when K were the Kronecker-Delta - in analogy to the above.)
In principal I want to support what Sean was indicating: Before applying any tool or algorithm one has to switch off the computer, take paper and pencil and think about true nature of the problem.
Henrik
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.
Hennrik,
On a completely separate note, how do you typset your post to include such nice math symbols?
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