A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem

A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a p...

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Main Authors: Shifang Tian, Xiaowei Liu, Ran An
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2021/9941692
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spelling doaj-42173d3401aa42dc8b126464e4009eb12021-08-30T00:00:45ZengHindawi LimitedMathematical Problems in Engineering1563-51472021-01-01202110.1155/2021/9941692A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic ProblemShifang Tian0Xiaowei Liu1Ran An2School of Mathematics and StatisticsSchool of Mathematics and StatisticsSchool of Mathematics and StatisticsIn this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a preconditioning approach is also used to ensure uniform convergence. Numerical experiments show that the method is first-order accuracy in time and almost third-order accuracy in space.http://dx.doi.org/10.1155/2021/9941692
collection DOAJ
language English
format Article
sources DOAJ
author Shifang Tian
Xiaowei Liu
Ran An
spellingShingle Shifang Tian
Xiaowei Liu
Ran An
A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem
Mathematical Problems in Engineering
author_facet Shifang Tian
Xiaowei Liu
Ran An
author_sort Shifang Tian
title A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem
title_short A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem
title_full A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem
title_fullStr A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem
title_full_unstemmed A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem
title_sort higher-order finite difference scheme for singularly perturbed parabolic problem
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1563-5147
publishDate 2021-01-01
description In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a preconditioning approach is also used to ensure uniform convergence. Numerical experiments show that the method is first-order accuracy in time and almost third-order accuracy in space.
url http://dx.doi.org/10.1155/2021/9941692
work_keys_str_mv AT shifangtian ahigherorderfinitedifferenceschemeforsingularlyperturbedparabolicproblem
AT xiaoweiliu ahigherorderfinitedifferenceschemeforsingularlyperturbedparabolicproblem
AT ranan ahigherorderfinitedifferenceschemeforsingularlyperturbedparabolicproblem
AT shifangtian higherorderfinitedifferenceschemeforsingularlyperturbedparabolicproblem
AT xiaoweiliu higherorderfinitedifferenceschemeforsingularlyperturbedparabolicproblem
AT ranan higherorderfinitedifferenceschemeforsingularlyperturbedparabolicproblem
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