Integrating a multi variable function numerically

Hey,

So I'm currently trying to explicitly integrate a function with four variables f(x,y,t,omega) w.r.t x and y.

The differential of omega is defined as a function of x,y,t and omega.

While initially I attempted to do this using the symbolic toolbox, unfortunately MATLAB is unable to integrate it explicitly and returns the corresponding error.

Is there a way to do this using quad() and clever use of functions, or perhaps an ODE solver?

Cheers,

Angus

[Roger Stafford]

There are a number of questions that need to be asked as to details in your problem.

1. Is the region you are integrating your function of four variables over, with respect to 'x' and 'y', a rectangle with sides parallel to the x and y axes, or is it some other kind of region?

2. As 'x' and 'y' vary in this region, do 't' and 'omega' remain constant or do one or both also vary?

3. You stated, "The differential of omega is defined as a function of x,y,t and omega". What exactly do you mean by that? If you mean "derivative", what variable is the derivative to be taken with respect to, and how does this tie in with the integration process?

4. The implication of the sentence in 3. seems to be that 'omega' varies as 'x' and 'y' vary. If so, in what way does it vary?

5. Can you please give the full code that you used in trying to use the symbolic toolbox to do the integration? That might answer many of the previous questions.

It should be pointed out that if the integration is to be performed numerically, then all parameters involved as well as integration limits need to be given specific numerical values. Only functions in the symbolic toolbox such as 'int' can give integrals involving symbolic parameters and limits.