Numerical integration for integrals 7th order.

Question

I need to calculate integral which looks like below, with some numerical method:

$\int\limits_{0}^{a}\int\limits_{0}^{\infty}\int\limits_{0}^{\infty}\int\limits_{0}^{\infty}\int\limits_{0}^{\infty}\int\limits_{0}^{\infty}\int\limits_{0}^{\infty}f(n_1, n_2, n_3, n_4, n_5, n_6, n_7) dn_1 dn_2 dn_3 dn_4 dn_5 dn_6 dn_7$

But, when I tried to find some numerical methods which can do it, I don't found anything. Also, I'm found Matlab some functions for simple integral, double, and triple integrals, but no functions for integrals with higher order. Same for scipy Python library.

Maybe anyone deal with same tasks, and tried to solve more than triple integrals with numerical methods?

Answer 1

One technique that may be useful is Monte-Carlo Integration. From the wikipedia page, "This method is particularly useful for higher dimensional integrals." The difficulty you may face is with the infinite limits on the inner integrals.

This may have some useful information.