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

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  • Guo, Pan
  • Wang, Na

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.

Suggested Citation

  • Guo, Pan & Wang, Na, 2026. "Asymptotic approximation of a class of second-order quasi-linear singularly perturbed boundary value problems with multiple turning points," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015486
    DOI: 10.1016/j.chaos.2025.117535
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