Journal of University of Chinese Academy of Sciences >
Computational Stability of Non-Conservative Schemes of Nonlinear Evolution Equations
Received date: 2003-01-24
Revised date: 2003-09-16
Online published: 2004-05-10
For the non conservative schemes of nonlinear evolution equations, taking two dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given. Based on the numerical tests, the relationship between the nonlinear computational stability, the construction of difference schemes, and the form of initial values is further discussed. It is proved through theoretical analysis and numerical tests that the computational stability of non conservative schemes is not only dependent on the structure of the scheme, but also on the form of initial values and their partial derivatives.
LIN WanTao . Computational Stability of Non-Conservative Schemes of Nonlinear Evolution Equations[J]. Journal of University of Chinese Academy of Sciences, 2004 , 21(3) : 402 -406 . DOI: 10.7523/j.issn.2095-6134.2004.3.019
[1] Lilly D K. On the computational stability of numerical solutions of time2dependent nonlinear geophysical fluid dynamics problems. Mon. Wea.Rev., 1965, 93(1): 11-26
[2] Arakawa A. Computational designfor long2term numerical integrationsof the equationsof atmospheric motion. J. Comp. Phys., 1966, 1: 119-143
[3] Jespersen P C. Arakawa’s method is a finite element method. J. Comp. Phys., 1974, 16: 383-390
[4] 曾庆存. 计算稳定性的若干问题. 大气科学, 1978, 2(3): 181-191
[5] 曾庆存, 季仲贞. 发展方程的计算稳定性问题. 计算数学, 1981, 3(1): 79-86
[6] 季仲贞. 二维Lilly 格式非线性计算不稳定的例子. 科学通报, 1980, 25(19): 890-892
[7] 季仲贞. 非线性计算稳定性的比较分析. 大气科学, 1981, 4(4): 344-354
[8] 季仲贞, 王斌. 再论发展方程差分格式的构造和应用. 大气科学, 1991, 15(2): 72-78
[9] 季仲贞, 王斌,曾庆存. 计算地球流体力学若干新进展. 空气动力学学报, 1998, 16(1): 108-114
[10] 季仲贞,杨晓忠,林万涛. 非线性计算不稳定问题的进一步研究. 中国科学院研究生院学报,2001,18(1): 59-65
[11] 王斌, 季仲贞. 显式完全平方守恒差分格式的构造及其初步检验. 科学通报, 1990, 35(10): 766-768
[12] 王斌, 季仲贞. 协调耗散算子与显式完全平方守恒差分格式. 中国科学(B 辑), 1993, 23(6): 665-672
[13] 王斌, 曾庆存,季仲贞. 平方守恒系统与 Hamilton 系统. 中国科学(A 辑), 1995, 25(7): 765-770
[14] 王斌, 季仲贞. 变步长显式完全平方守恒差分格式. 气象学报, 1995, 53(3): 299-305
[15] 陈嘉滨,季仲贞. 半拉格朗日平方守恒计算格式的研究. 大气科学,2001, 25(6): 837-846
[16] Ji Zhong-Zhen, Wang Bin, Zhao Ying, et al. Total energy conservation and the symplectic algorithm. Advance in Atmospheric Sciences, 2002, 19(3): 459-469
[17] 林万涛, 季仲贞,王斌. 一种判定非线性发展方程差分格式计算稳定性的新方法. 科学通, 2000, 45(8): 881-885
[18] 林万涛, 季仲贞,李双林. 线性与非线性发展方程差分格式计算稳定性的比较分析. 自然科学进展, 2000, 10(10): 936-940
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