A second order scheme for a time-dependent, singularly perturbed convection-diffusion equation

DOI10.1016/S0377-0427(01)00502-7zbMath1007.65075MaRDI QIDQ1612329

Wim Lenferink

Publication date: 22 August 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergencenumerical examplesingular perturbationinitial-boundary value problemfinite elementsconvection-diffusion equationerror boundBakhvalov-Shishkin mesh

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (11)

Parameter-robust numerical method for time-dependent weakly coupled linear system of singularly perturbed convection-diffusion equations ⋮ An efficient wavelet-based collocation method for handling singularly perturbed boundary-value problems in fluid mechanics ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Numerical analysis for a class of coupled system of singularly perturbed time‐dependent convection‐diffusion equations with a discontinuous source term ⋮ A new numerical algorithm for time-dependent singularly perturbed differential-difference convection-diffusion equation arising in computational neuroscience ⋮ An operational Haar wavelet collocation method for solving singularly perturbed boundary-value problems ⋮ Unnamed Item ⋮ Numerical solutions of singularly perturbed one-dimensional parabolic convection-diffusion problems by the Bessel collocation method ⋮ A fitted operator finite difference method of lines for singularly perturbed parabolic convection-diffusion problems ⋮ Numerical solution of singularly perturbed problems using Haar wavelet collocation method ⋮ A layer adaptive B-spline collocation method for singularly perturbed one-dimensional parabolic problem with a boundary turning point

Cites Work

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• A study of difference schemes with the first derivative approximated by a central difference ratio
• The midpoint upwind scheme
• An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
• Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh
• Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection-diffusion problem
• Iterative Solution Methods
• Locally one-dimensional difference schemes for singularly perturbed parabolic equations with convective terms
• -uniform schemes with high-order time-accuracy for parabolic singular perturbation problems

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