Approximation of derivatives in a convection-diffusion two-point boundary value problem

DOI10.1016/S0168-9274(01)00051-4zbMath0987.65069OpenAlexW2039239752MaRDI QIDQ5948559

Natalia Kopteva, Martin Stynes

Publication date: 8 November 2001

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00051-4

zbMATH Keywords

numerical resultsconvection-diffusion equationerror boundstwo-point boundary value problemBakhvalov meshShishkin meshupwind conservative finite difference scheme

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

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• The computation of boundary flow with uniform accuracy with respect to a small parameter
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• On the Approximation of Derivatives of Singularly Perturbed Boundary Value Problems
• A Conservative Uniformly Accurate Difference Method for a Singular Perturbation Problem in Conservation Form
• On the Uniform Convergence of the Scharfetter–Gummel Discretization in One Dimension
• Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
• Defect correction on Shishkin-type meshes