A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

Dingwen Deng; Jianqiang Xie; Yaolin Jiang; Dong Liang

doi:10.1080/00207160.2018.1542133

A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

Dingwen Deng
, Jianqiang Xie
, Yaolin Jiang
, Dong Liang

School of Mathematics and Statistics

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

6 Scopus citations

Abstract

In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. By the discrete energy method, it is shown that the difference scheme is uniquely solvable, and has a convergence rate of O(∆t² + h²) with respect to L² - norm in constrained and non-constrained temporal grids. Besides, for constrained temporal step, a Richardson extrapolation method (REM) used along with the box scheme, which makes final solution third-order accurate in both time and space, is developed in detail. Finally, numerical results confirm the accuracy and efficiency of our solvers.

Original language	English
Pages (from-to)	1879-1898
Number of pages	20
Journal	International Journal of Computer Mathematics
Volume	96
Issue number	9
DOIs	https://doi.org/10.1080/00207160.2018.1542133
State	Published - 2 Sep 2019

Keywords

Neumann boundary conditions
Nonlinear convection-diffusion equations with delays
box scheme
convergence
solvability

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10.1080/00207160.2018.1542133

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title = "A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions",

abstract = "In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. By the discrete energy method, it is shown that the difference scheme is uniquely solvable, and has a convergence rate of O(∆t2 + h2) with respect to L2 - norm in constrained and non-constrained temporal grids. Besides, for constrained temporal step, a Richardson extrapolation method (REM) used along with the box scheme, which makes final solution third-order accurate in both time and space, is developed in detail. Finally, numerical results confirm the accuracy and efficiency of our solvers.",

keywords = "Neumann boundary conditions, Nonlinear convection-diffusion equations with delays, box scheme, convergence, solvability",

author = "Dingwen Deng and Jianqiang Xie and Yaolin Jiang and Dong Liang",

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T1 - A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

AU - Deng, Dingwen

AU - Xie, Jianqiang

AU - Jiang, Yaolin

AU - Liang, Dong

PY - 2019/9/2

Y1 - 2019/9/2

N2 - In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. By the discrete energy method, it is shown that the difference scheme is uniquely solvable, and has a convergence rate of O(∆t2 + h2) with respect to L2 - norm in constrained and non-constrained temporal grids. Besides, for constrained temporal step, a Richardson extrapolation method (REM) used along with the box scheme, which makes final solution third-order accurate in both time and space, is developed in detail. Finally, numerical results confirm the accuracy and efficiency of our solvers.

AB - In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. By the discrete energy method, it is shown that the difference scheme is uniquely solvable, and has a convergence rate of O(∆t2 + h2) with respect to L2 - norm in constrained and non-constrained temporal grids. Besides, for constrained temporal step, a Richardson extrapolation method (REM) used along with the box scheme, which makes final solution third-order accurate in both time and space, is developed in detail. Finally, numerical results confirm the accuracy and efficiency of our solvers.

KW - Neumann boundary conditions

KW - Nonlinear convection-diffusion equations with delays

KW - box scheme

KW - convergence

KW - solvability

UR - https://www.scopus.com/pages/publications/85056152148

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DO - 10.1080/00207160.2018.1542133

M3 - 文章

AN - SCOPUS:85056152148

SN - 0020-7160

VL - 96

SP - 1879

EP - 1898

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 9

ER -

A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

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