The Stokes phenomenon for a linear differential system with an irregular singularity at 0 in complex domain is the phenomenon of the discontinuity of analytic solutions asymptotic to a same formal solution. In general, there are certain directions beyond which a given asymptotic expansion becomes invalid. Such directions are called Stokes directions. A general procedure exists to uniquely associate an actual asymptotic solution with a given formal one in any direction called anti-Stokes directions. To each anti-Stokes direction there is a Stokes matrix which is a meromorphic invariant for the system.The Stokes matrices are, in general, transcendental with respect to the coefficients of the differential system.So Numerical calculation are of interest. I introduce one of numerical calculations of the Stokes matrix.
Seminar on Analysis at University of Tsukuba