Stability condition for difference schemes for parabolic systems

Weiwei SUN; Guangwei Yuan

doi:10.1137/S0036142998348182

Stability condition for difference schemes for parabolic systems

Weiwei SUN
, Guangwei Yuan

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

29 Downloads (CityUHK Scholars)

Abstract

Recently, Goldberg studied in [M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 478-493, M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 1995-2003] stability conditions of a well-known family of difference schemes for the following multidimensional parabolic system of second order:

∂u(x, t)/∂t = ∑_{1≤p≤q≤s} A_pq ∂²u(x, t)/∂x_p∂x_q+ ∑_1≤p≤sB_p∂u(x, t)/∂x_p+ Cu(x, t).

Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.

Original language	English
Pages (from-to)	548-555
Journal	SIAM Journal on Numerical Analysis
Volume	38
Issue number	2
Online published	19 Jul 2000
DOIs	https://doi.org/10.1137/S0036142998348182
Publication status	Published - 2000

Research Keywords

Difference schemes
Parabolic systems
Stability

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2000 Society for Industrial and Applied Mathematics.

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title = "Stability condition for difference schemes for parabolic systems",

abstract = "Recently, Goldberg studied in [M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 478-493, M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 1995-2003] stability conditions of a well-known family of difference schemes for the following multidimensional parabolic system of second order: ∂u(x, t)/∂t = ∑1≤p≤q≤s Apq ∂2u(x, t)/∂xp∂xq + ∑1≤p≤s Bp ∂u(x, t)/∂xp + Cu(x, t). Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.",

keywords = "Difference schemes, Parabolic systems, Stability",

author = "Weiwei SUN and Guangwei Yuan",

year = "2000",

doi = "10.1137/S0036142998348182",

language = "English",

volume = "38",

pages = "548--555",

journal = "SIAM Journal on Numerical Analysis",

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publisher = "Society for Industrial and Applied Mathematics",

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TY - JOUR

T1 - Stability condition for difference schemes for parabolic systems

AU - SUN, Weiwei

AU - Yuan, Guangwei

PY - 2000

Y1 - 2000

N2 - Recently, Goldberg studied in [M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 478-493, M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 1995-2003] stability conditions of a well-known family of difference schemes for the following multidimensional parabolic system of second order: ∂u(x, t)/∂t = ∑1≤p≤q≤s Apq ∂2u(x, t)/∂xp∂xq + ∑1≤p≤s Bp ∂u(x, t)/∂xp + Cu(x, t). Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.

AB - Recently, Goldberg studied in [M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 478-493, M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 1995-2003] stability conditions of a well-known family of difference schemes for the following multidimensional parabolic system of second order: ∂u(x, t)/∂t = ∑1≤p≤q≤s Apq ∂2u(x, t)/∂xp∂xq + ∑1≤p≤s Bp ∂u(x, t)/∂xp + Cu(x, t). Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.

KW - Difference schemes

KW - Parabolic systems

KW - Stability

UR - https://www.scopus.com/pages/publications/0034448457

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0034448457&origin=recordpage

U2 - 10.1137/S0036142998348182

DO - 10.1137/S0036142998348182

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1429

VL - 38

SP - 548

EP - 555

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 2

ER -

Stability condition for difference schemes for parabolic systems

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