A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations

DOI10.1016/j.camwa.2004.06.015zbMath1070.65065OpenAlexW2034516524MaRDI QIDQ1767880

Xianqiang Yang

Publication date: 8 March 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2004.06.015

zbMATH Keywords

singular perturbationasymptotic expansionnumerical examplesfinite difference schemeboundary layerfourth-order equationexponentially fittingnon-selfadjoint boundary value problem

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Sequential estimation (62L12) Singular perturbations for ordinary differential equations (34E15)

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Cites Work

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• Numerical treatment of singularly perturbed two point boundary value problems
• Approximate method for the numerical solution of singular perturbation problems
• Numerical solution of singular perturbation problems via deviating arguments
• Die gleichmäßige Stabilität singulär gestörter diskreter und kontinuierlicher Randwertprobleme
• Asymptotic numerical methods for singularly perturbed fourth-order ordinary differential equations of reaction-diffusion type
• Further examples of the boundary value technique in singular perturbation problems
• Singular perturbation problems for systems of partial differential equations of elliptic type
• A boundary value technique for singular perturbation problems
• Singular perturbation methods for ordinary differential equations
• A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers
• Singularly perturbed higher order boundary value problems
• A numerical method for boundary value problems for singularly perturbed fourth-order ordinary differential equations
• A computational method are solving boundary value problems for third-order singularly perturbed ordinary differential equations
• A computational method for solving singular perturbation problems
• Singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations
• The Asymptotic Solution of a Class of Third-Order Boundary Value Problems Arising in the Theory of Thin Film Flows
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Sufficient Conditions for Uniform Convergence of a Class of Difference Schemes for a Singularly Perturbed Problem
• Differential Inequalities of Higher Order and the Asymptotic Solution of Nonlinear Boundary Value Problems
• Locking in finite-element approximations to long thin extensible beams
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
• Boundary Value Technique for Finding Numerical Solution to Boundary Value Problems for Third Order Singularly Perturbed Ordinary Differential Equations