Partial differential equations, Mathematical physics
First-order general differential equation for multi-level asymptotics at higher levels and recurrence relationship of singulants
Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1267-1278.

We construct a relation between the leading pre-factor function A(z) and the singulants u 0 (z), u 1 (z), and recurrence relation of the singulants at higher levels for the solution of singularly-perturbed first-order ordinary general differential equation with a small parameter via the method of multi-level asymptotics. The particular equation is chosen due to its appearance at every level of multi-level asymptotic approach for the first-order differential equations. By the relations derived by the asymptotic analysis from the equation, Stokes and anti-Stokes lines can be extracted more quickly and so which exponentials of the expansions are actually contributed in each sector of the complex plane can be deduced faster. Multi-level asymptotic analysis of the first-order singular equations and the Stokes phenomenon may be done straightaway from the higher levels of the analysis.

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DOI: 10.5802/crmath.264
Classification: 34M40, 34E20
Say, Fatih 1

1 Department of Mathematics, Faculty of Arts and Sciences, Ordu University, Ordu, Turkey
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Say, Fatih. First-order general differential equation for multi-level asymptotics at higher levels and recurrence relationship of singulants. Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1267-1278. doi : 10.5802/crmath.264. http://www.numdam.org/articles/10.5802/crmath.264/

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