Hi Daniel,

I apologize for the inappropriate subject header. Thanks for the reply!

Best regards,

Stven

Hi Rene, Thanks so much for you very detailed reply!! Very appreciated. I am really busy recently, so I will follow your steps to do the calculation late today. Hope I won't get stuck. Thanks again! Best regards, Stven

Use NIntegrate to compute r[x] (here I use Mathematica notation and avoid capitalizing user-defined function names). Compute the integral of r[x]*f[x] also with NIntegrate (possibly it should just be done as a double integral). At that point you are pretty much done.

I should remark that the subject header seems to be incorrect; I have not found a specific example anywhere in this.

Hi Rene, Thanks a million for your reply. I am very new to Mathematica, also I have never used any other maths software like Matlab before. Would you mind to write down some relevant codes for this calculation? I will write down the steps that I don't know how to code. It will be greatly appreciated if you can provide any help.

-----Let's suppose that there is a function, R(x), with variable x, and R(x)= ? P(x,t) dt. P(x,t) is a function of x and t-----

How to define P as a function of x and t? Will mathematica be able to compute this integral given a small region like {t, t+0.1)

----- Make a "sufficiently dense" () grid of points {x0, y0} in the (x,y}-plane----*

How to define a grid? Can you show me the code for it? Will the grid in Mathematica be able to store an equation?

When I successfully calculate the integral for each interval, {t, t+0.1}, how do I sum it to get R(x)? I may have a million equations stored in the grid and the sum of them, which gives me R(x), will be horrendous.

Thanks again for any help if you can provide!!

Best regards,

Stven

Hi Stven,

The only thing I can think of is a rather brute-force and decidedly unelegant method: 1. Make a "sufficiently dense" (*) grid of points {x0, y0} in the (x,y}-plane. 2. Calculate your function H(x,y) on this grid. (3. This step is optional: Perhaps wrap an Interpolation command over the H(x,y} so as to get smooth connections between the grid points.) 4. Choose your fixed point x0 and plot H(x0, y) versus y.

This is how I would try it. Almost certainly there are more efficient methods, but this is simple and I don't see why it wouldn't work.

(*) Footnote re point 1: The "sufficiently dense" is the stumbling block of course. If you know next to nothing about H(x,y), you'll have to proceed by trial and error. The more you know about H, the smarter you can choose your grid: make the grid sparse in regions where H doesn't change much and dense in regions with dramatic gradients.

Hope this works for you.

René Samson