  We propose a new method for the evaluation of intersection numbers for
twisted meromorphic $n$-forms, through Stokes' theorem in $n$ dimensions. It is
based on the solution of an $n$-th order partial differential equation and on
the evaluation of multivariate residues. We also present an algebraic
expression for the contribution from each multivariate residue. We illustrate
our approach with a number of simple examples from mathematics and physics.
