0
|
5630 Views
|
8 Replies
|
6 Total Likes
View groups...
Share
GROUPS:

# Integral equations in Wolfram Language

Posted 9 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): 8 Replies
Sort By:
Posted 9 years ago
 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?
Posted 9 years ago
 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 9 years ago
 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 9 years ago
 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 9 years ago
 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
Posted 9 years ago
 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 9 years ago
 Hennrik, On a completely separate note, how do you typset your post to include such nice math symbols?
Posted 9 years ago
 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 helpfulAndrei D. Polyanin, Alexander V. Manzhirov; Handbook of Integral EquationsHenrik