ar X iv : h ep - p h / 02 11 17 8 v 1 1 2 N ov 2 00 2 1 Numerical evaluation of master integrals from differential equations ∗

The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman graph. The particular case of the general massive 2-loop sunrise self-mass diagram is analyzed. The method offers a reliable and robust approach to the direct and precise numerical evaluation of master integrals.