On the Asymptotic Behavior of the Solutions of Nearly Regular Singular Differential Equations
Year: 2026
Type: article
Abstract: In this paper we consider families of differential equations on some real interval that depend on a parameter $$\varepsilon $$ ε , are regular for $$\varepsilon \ne 0$$ ε ≠ 0 and have exactly one regular singular point for $$\varepsilon =0$$ ε = 0 . Our aim is to give a formula which describes the asymptotic behavior of the solutions for $$\varepsilon \rightarrow 0$$ ε → 0 . To this end, we use a method that combines matched asymptotic analysis with uniform asymptotic integration. We then apply our results to some typical examples, such as a differential equation with two coalescing regular singular points as well as a singular perturbation of the Bessel equation.
Source: Results in Mathematics
Author: Harald Schmid
Institution: Ostbayerische Technische Hochschule Amberg-Weiden
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7155544484