Numerical 4th order integration in matlab

[SimonePirrotta]

Hi everybody,
i hope that someone can help me in performing the numerical integration of a 4-variables function: in matlab i've found the fuction "triplequad" which allows to work until 3rd order... what can i do?

Thanks a lot!

SP

 

[Marco83]

It sounds to me like you are making some confusion between number of variables and order of the integration.

What you are looking for is not a 4th order method, but just a general method to integrate a 4 variables function.

The order of an integrating scheme/method refers to the order of magnitude of the neglected terms (truncation error).

I think matlab does not have any embedded function for integration of functions of more than 3 variables, nonetheless you can write your own integrating algorithm.

Take any numerical analisys book. There you should find integration methods for at least 2 variables. Go up to 4 in a hyper-rectangular domain (that is what matlab handles)is a mere exercise of extrapolation from the latter.

Although traditional methods will work, , they will involve at least 4 for cycles, and this will result in a very slow integration process. What I would suggest you is to check out some Monte Carlo integration schemes; these schemes use a statistical approach to the calculation of the integral and they are intrinsically multidimensional. The only drawback is the low accuracy obtainable in a reasonable time.