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On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation. (English) Zbl 1058.34123
The author considers the particular integral of the differential equation d 2 w/dz 2 +u 2 z 2 w=e iu((1/2)z 2 -4z) , where u is a large parameter. He determines the complete Stokes geometry, i.e., the active and inactive Stokes curves and the higher-order Stokes curve. (A Stokes curve to be inactive or a Stokes multiplier to change its value are events typical for higher-order Stokes phenomena.) He presents numerical examples and suggests how the study can be extended to more complicated problems.
MSC:
34M40Stokes phenomena and connection problems (ODE in the complex domain)
34E05Asymptotic expansions (ODE)
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)