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Zbl 1058.34123
Olde Daalhuis, A.B.
On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation. (English)
[J] J. Comput. Appl. Math. 169, No. 1, 235-246 (2004). ISSN 0377-0427

The author considers the particular integral of the differential equation $d^2w/dz^2+u^2z^2w=e^{iu((1/2)z^2-4z)}$, 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.
[Vladimir P. Kostov (Nice)]

MSC 2000:: *34M40 Stokes phenomena and connection problems
34E05 Asymptotic expansions (ODE)
34E20 Asymptotic singular perturbations, methods (ODE)

Keywords: asymptotic expansions; connection formulae; inhomogeneous differential equations; Stokes phenomenon; Stokes multiplier; turning points

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