Asymptotic approximation of a class of second-order quasi-linear singularly perturbed boundary value problems with multiple turning points

Pan Guo and Na Wang

Chaos, Solitons & Fractals, 2026, vol. 202, issue P2

Abstract: In this article, we discuss a class of second-order quasi-linear singular perturbation boundary value problems with εy″−x−ax−bεny+1y′−x−ay=0. We notice that this problem contains two kinds of turning points, the first is x=a and x=b, the second is x∗εny0x∗+1=0, y0 is the degenerate solution. For this problem, we have derived that it is not necessarily true that for a fixed value of ε, a larger n yields a smaller discrepancy between the asymptotic approximation and numerical results. Utilizing the method of matched asymptotic expansions, asymptotic solutions featuring a boundary layer at the endpoint and an interior shock layer have been constructed. With the aid of the differential inequality theorem, the existence of solutions and error estimates are established. Finally, numerical examples are presented to validate the theoretical results.

Keywords: Singular perturbation; Turning point; Matching method; Shock solution; Differential inequality (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015486

DOI: 10.1016/j.chaos.2025.117535

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