The \(\varepsilon\)-uniform convergence of a defect correction method on a Shishkin mesh

DOI10.1016/S0168-9274(00)00026-XzbMath0978.65069OpenAlexW2013275949MaRDI QIDQ5932817

Anja Fröhner, Hans-Goerg Roos

Publication date: 21 January 2002

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(00)00026-x

zbMATH Keywords

convergencesingular perturbationnumerical experimentsfinite difference schemeboundary value problemShishkin meshdefect correction method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (8)

Richardson extrapolation for a convection--diffusion problem using a Shishkin mesh ⋮ \(\epsilon\) -uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general ddes ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Layer-adapted meshes for convection-diffusion problems ⋮ The ε-Uniform Convergence of a Defect-Correction Method on a Shishkin Mesh ⋮ Unnamed Item ⋮ \(\varepsilon\)-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems ⋮ THE PARAMETER-ROBUST NUMERICAL METHOD BASED ON DEFECT-CORRECTION TECHNIQUE FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH LAYER BEHAVIOR

Cites Work

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• The midpoint upwind scheme
• The uniform convergence with respect to a small parameter of A. A. Samarskij's monotone scheme and its modification
• Adaptive refinement for convection-diffusion problems based on a defect-correction technique and finite difference method
• An Analysis of a Defect-Correction Method for a Model Convection-Diffusion Equation
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Layer-Adapted Grids for Singular Perturbation Problems

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