I want to solve an integral that is of a following form in Matlab:
$\int_{r}\int_{t} r e^{i * (F(r,t)x + G(r,t)y + H(r,t)z)} drdt$
I used to be able to find a surface fit in matlab for the F, G, and H functions, but am moving into more complex domains where these values can not be as easily written explicitly (they are defined by other physics not explained here since it isn't very important to the actual question). This was previously done using Integral2.
For my more complex scenarios which cannot be defined in a closed form, I want to transition my code to use TRAPZ.
I can find the values of F, G, and H, across the entire domain, which I can define as a square domain that is R x R, where R is the maximum value of the circle r. In this matrix, since it is square, I am then defining the values outside of my circular bounds to be 0. So, I am forcing the surfaces that form F, G, and, H, to have a circular boundary.
I am doing this so that I can use the TRAPZ function in Matlab. I have not been able to find implementations of TRAPZ for circular coordinates like this problem. I can re-write my functions and bounds in terms of cartesian coordinates, which is what I have currently. However, this result is not working so I am not sure how else to implement this. Thanks!