The controversial stability analysis

被引：26
作者：
Sousa, E [1 ]
机构：
[1] Univ Coimbra, Dept Matemat, P-3000 Coimbra, Portugal
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2003年 / 145卷 / 2-3期
关键词：
stability analysis; convection-diffusion; finite differences;
D O I：
10.1016/S0096-3003(03)00274-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this review we present different techniques for obtaining stability limits for a finite difference scheme-the forward-time and space-centered numerical scheme applied to the convection-diffusion equation. A survey of past attempts to state stability conditions for this scheme illustrates the difficulties in stability analysis that arise as soon as a scheme becomes more complex and illuminates the concepts of necessary and sufficient conditions for stability. (C) 2003 Elsevier Inc. All rights reserved.
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收藏
页码：777 / 794
页数：18
相关论文
共 20 条
[1]  
[Anonymous], 1972, COMPUTATIONAL FLUID
[2]   GENERAL FINITE-DIFFERENCE FORMULATION WITH APPLICATION TO NAVIER-STOKES EQUATIONS [J].
CHIEN, JC .
JOURNAL OF COMPUTATIONAL PHYSICS, 1976, 20 (03) :268-278
[3]  
CLANCY RM, 1981, MON WEATHER REV, V109, P1807, DOI 10.1175/1520-0493(1981)109<1807:ANOFDO>2.0.CO
[4]  
2
[5]   ON PARTIAL DIFFERENCE EQUATIONS OF MATHEMATICAL PHYSICS [J].
COURANT, R ;
FRIEDRICHS, K ;
LEWY, H .
IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1967, 11 (02) :215-+
[6]   Partial differential equations of mathematical physics [J].
Courant, R ;
Friedrichs, K ;
Lewy, H .
MATHEMATISCHE ANNALEN, 1928, 100 :32-74
[7]  
FROMM JE, 1964, METHODS COMPUTATIONA, V3, P345
[8]   ANALYSIS OF ERROR GROWTH FOR EXPLICIT DIFFERENCE-SCHEMES IN CONDUCTION-CONVECTION PROBLEMS [J].
GRIFFITHS, DF ;
CHRISTIE, I ;
MITCHELL, AR .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1980, 15 (07) :1075-1081
[9]   THE STABILITY OF EXPLICIT EULER TIME-INTEGRATION FOR CERTAIN FINITE-DIFFERENCE APPROXIMATIONS OF THE MULTI-DIMENSIONAL ADVECTION DIFFUSION EQUATION [J].
HINDMARSH, AC ;
GRESHO, PM ;
GRIFFITHS, DF .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1984, 4 (09) :853-897
[10]  
Hirt C, 1968, J COMPUT PHYS, V2, P339, DOI DOI 10.1016/0021-9991(68)90041-7
12