On the calculation of Stokes multipliers for linear differential equations of the second order

Abstract

TWO new methods are described for the computation of connection coefficients for the asymptotic solutions of linear second-order differential equations having an irregular singularity of arbitrary rank. The first method is based on new asymptotic expansions of the higher coefficients in the asymptotic solutions. The second method is based on direct numerical solution of the differential equation. Numerical examples are included.