Asymptotic solutions of singularly perturbed second-order differential equations and application to multi-point boundary value problems

DOI10.1016/j.aml.2010.04.021zbMath1200.34061OpenAlexW2033546847MaRDI QIDQ988704

Lingju Kong, Zeng-Ji Du

Publication date: 18 August 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2010.04.021

zbMATH Keywords

singular perturbationasymptotic solutionsLiouville-Green transformmulti-point boundary value problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05)

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A new reproducing kernel method for linear nonlocal boundary value problems ⋮ Iterative analytic approximation to nonlinear convection dominated systems ⋮ A second order numerical method for singularly perturbed problem with non-local boundary condition ⋮ ROBUST NUMERICAL METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION TYPE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITION ⋮ Exponential fitted operator method for singularly perturbed convection-diffusion type problems with nonlocal boundary condition ⋮ An efficient numerical algorithm based on Haar wavelet for solving a class of linear and nonlinear nonlocal boundary-value problems ⋮ An optimal reproducing kernel method for linear nonlocal boundary value problems ⋮ Second-order differential equation with indefinite and repulsive singularities ⋮ Unnamed Item ⋮ Green's function and positive solutions for a second-order singular boundary value problem with integral boundary conditions and a delayed argument

Cites Work

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• Singular perturbation methods for ordinary differential equations
• On the existence of \(m\)-point boundary value problem at resonance for higher order differential equation.
• Least squares methods for solving differential equations using Bézier control points.
• Multi-point boundary value problems of second-order differential equations. I
• Singular perturbations for third-order nonlinear multi-point boundary value problem

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