Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem

Natalia Kopteva; Torsten Linß

doi:10.1016/S0377-0427(01)00353-3

Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem

Natalia Kopteva
, Torsten Linß

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

A singularly perturbed quaslinear two-point boundary value problem with an exponential boundary layer is considered. The problem is discretized using the standard central difference scheme on generalized Shishkin-type meshes. We give a uniform second-order error estimate in a discrete L∞ norm. Numerical experiments support the theoretical results.

Original language	English (Ireland)
Pages (from-to)	257-267
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	137
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(01)00353-3
Publication status	Published - 15 Dec 2001

Keywords

Central difference scheme
Convection-diffusion problems
Quasilinear problems
Shishkin-type mesh
Singular perturbation

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10.1016/S0377-0427(01)00353-3

Cite this

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title = "Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem",

abstract = "A singularly perturbed quaslinear two-point boundary value problem with an exponential boundary layer is considered. The problem is discretized using the standard central difference scheme on generalized Shishkin-type meshes. We give a uniform second-order error estimate in a discrete L∞ norm. Numerical experiments support the theoretical results.",

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T1 - Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem

AU - Kopteva, Natalia

AU - Linß, Torsten

PY - 2001/12/15

Y1 - 2001/12/15

N2 - A singularly perturbed quaslinear two-point boundary value problem with an exponential boundary layer is considered. The problem is discretized using the standard central difference scheme on generalized Shishkin-type meshes. We give a uniform second-order error estimate in a discrete L∞ norm. Numerical experiments support the theoretical results.

AB - A singularly perturbed quaslinear two-point boundary value problem with an exponential boundary layer is considered. The problem is discretized using the standard central difference scheme on generalized Shishkin-type meshes. We give a uniform second-order error estimate in a discrete L∞ norm. Numerical experiments support the theoretical results.

KW - Central difference scheme

KW - Convection-diffusion problems

KW - Quasilinear problems

KW - Shishkin-type mesh

KW - Singular perturbation

UR - https://www.scopus.com/pages/publications/0035892575

U2 - 10.1016/S0377-0427(01)00353-3

DO - 10.1016/S0377-0427(01)00353-3

M3 - Article

AN - SCOPUS:0035892575

SN - 0377-0427

VL - 137

SP - 257

EP - 267

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem

Abstract

Keywords

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