A high-order finite difference scheme for a singularly perturbed fourth-order ordinary differential equation

DOI10.1080/00207160.2017.1339869zbMath1499.65317OpenAlexW2624475384WikidataQ115314907 ScholiaQ115314907MaRDI QIDQ5028562

Zhongdi Cen, Anbo Le, Aimin Xu

Publication date: 10 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2017.1339869

zbMATH Keywords

singular perturbationuniform convergencefinite difference schemeShishkin meshfourth-order ordinary differential equation

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (3)

Spline-based parameter-uniform scheme for fourth-order singularly perturbed differential equations ⋮ Uniformly convergent scheme for fourth-order singularly perturbed convection-diffusion ODE ⋮ Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

Cites Work

• Unnamed Item
• An improved uniformly convergent scheme in space for 1D parabolic reaction-diffusion systems
• An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations
• A brief survey on numerical methods for solving singularly perturbed problems
• High order robust approximations for singularly perturbed semilinear systems
• A coupled system of singularly perturbed parabolic reaction-diffusion equations
• An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems
• Robust convergence of a compact fourth-order finite difference scheme for reaction-diffusion problems
• Layer-adapted meshes for reaction-convection-diffusion problems
• Uniform fourth order difference scheme for a singular perturbation problem
• A numerical method for a system of singularly perturbed reaction-diffusion equations
• A numerical method for boundary value problems for singularly perturbed fourth-order ordinary differential equations
• Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations
• A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems
• A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems
• Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations
• Second order parameter-uniform convergence for a finite difference method for a singularly perturbed linear parabolic system
• A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations
• A parameter‐robust numerical method for a system of reaction–diffusion equations in two dimensions
• A higher-order scheme for quasilinear boundary value problems with two small parameters

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