  We give an approximate algorithm of computing holonomic systems of linear
differential equations for definite integrals with parameters. We show that
this algorithm gives a correct answer in finite steps, but we have no general
stopping condition. We apply the approximate method to find differential
equations for integrals associated to smooth Fano polytopes. They are
interested in the study of K3 surfaces and the toric mirror symmetry. In this
class of integrals, we can apply Stienstra's rank formula to our algorithm,
which gives a stopping condition of the approximate algorithm.
