Rethinking of the Finite Difference Time-Step Integrations

Wanxie Zhong; Jianping Zhu

doi:10.1007/BF02453396

Rethinking of the Finite Difference Time-Step Integrations

Wanxie Zhong, Jianping Zhu

Mississippi State University

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

Abstract

The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However, when the time step becomes longer, it causes the problem of numerical instability. The explicit integration schemes derived by the single point precise integration method given in this paper are proved unconditionally stable. Comparisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and convective-diffusion equations. Numerical examples show the superiority of the single point integration method.

Original language	American English
Journal	Applied Mathematics and Mechanics
Volume	16
DOIs	https://doi.org/10.1007/BF02453396
State	Published - Aug 1 1995

Keywords

finite difference method
time step integration
numerical stability

Disciplines

Applied Mathematics

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10.1007/BF02453396License: CC BY

Cite this

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title = "Rethinking of the Finite Difference Time-Step Integrations",

abstract = " The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However, when the time step becomes longer, it causes the problem of numerical instability. The explicit integration schemes derived by the single point precise integration method given in this paper are proved unconditionally stable. Comparisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and convective-diffusion equations. Numerical examples show the superiority of the single point integration method.",

keywords = "finite difference method, time step integration, numerical stability",

author = "Wanxie Zhong and Jianping Zhu",

note = "Zhong, W. and Zhu, J. (1995). Rethinking of the Finite Difference Time-Step Integrations. Applied Mathematics and Mechanics, 16(8), 705-711, doi: 10.1007/BF02453396.",

year = "1995",

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doi = "10.1007/BF02453396",

language = "American English",

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T1 - Rethinking of the Finite Difference Time-Step Integrations

AU - Zhong, Wanxie

AU - Zhu, Jianping

N1 - Zhong, W. and Zhu, J. (1995). Rethinking of the Finite Difference Time-Step Integrations. Applied Mathematics and Mechanics, 16(8), 705-711, doi: 10.1007/BF02453396.

PY - 1995/8/1

Y1 - 1995/8/1

N2 - The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However, when the time step becomes longer, it causes the problem of numerical instability. The explicit integration schemes derived by the single point precise integration method given in this paper are proved unconditionally stable. Comparisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and convective-diffusion equations. Numerical examples show the superiority of the single point integration method.

AB - The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However, when the time step becomes longer, it causes the problem of numerical instability. The explicit integration schemes derived by the single point precise integration method given in this paper are proved unconditionally stable. Comparisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and convective-diffusion equations. Numerical examples show the superiority of the single point integration method.

KW - finite difference method

KW - time step integration

KW - numerical stability

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/70

UR - http://journals.ohiolink.edu/ejc/article.cgi?issn=02534827&issue=v16i0008&article=705_rtfdti

U2 - 10.1007/BF02453396

DO - 10.1007/BF02453396

M3 - Article

VL - 16

JO - Applied Mathematics and Mechanics

JF - Applied Mathematics and Mechanics

ER -

Rethinking of the Finite Difference Time-Step Integrations

Abstract

Keywords

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