Numerical evaluation of some master integrals for the 2-loop general massive self-mass 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. Some results obtained for the 2-loop self-mass MI are reviewed. The method offers a reliable and robust approach to the direct and precise numerical evaluation of master integrals.