On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation

In this paper we discuss the higher-order Stokes phenomenon of the particular integral of an inhomogeneous linear ordinary differential equation with a large parameter. We determine the complete Stokes geometry, that are all the active and inactive Stokes curves, and the higher-order Stokes curve. The main tool that we use is the growth of the coefficients in the dominating divergent asymptotic expansion of the particular integral. We also discuss a strategy that might work in more complicated problems.