First-order general differential equation for multi-level asymptotics at higher levels and recurrence relationship of singulants
In this article, the author is interested in the singularly perturbed first-order ordinary differential equation \[ \varepsilon\dfrac{dy}{dz}+A(z)y=f(z) \] with a small positive parameter \(\varepsilon\). He investigates the asymptotic behavior of its formal power series solution in \(\varepsilon\), and aims to locate and study its Stokes and anti-Stokes lines. The approach developed by the author is based on the method of multi-level asymptotics introduced in [\textit{F. Say}, Exponential asymptotics: multi-level asymptotics of model problems. University of Nottingham (PhD Thesis) (2016)], a method which is similar to the methods already used in hyperasymptotics (see [\textit{M. V. Berry} and \textit{C. J. Howls}, Proc. R. Soc. Lond., Ser. A 430, No. 1880, 653--668 (1990; Zbl 0745.34052)] for instance).
singularly perturbed differential equation
scientific article; zbMATH DE number 7468760
scientific article