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Volume 19 Issue 4

Jul.  2002

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2002 >  19(4): 699-704

A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations

  • 1.

    LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029


doi: 10.1007/s00376-002-0009-9

  • For several difference schemes of linear and non-linear evolution equations, taking the one-dimensional linear and non-linear advection equations as examples, a comparative analysis for computational stability is carried out and the relationship between non-linear computational stability, the construction of difference schemes, and the form of initial values is discussed. It is proved through comparative analysis and numerical experiment that the computational stability of the difference schemes of the non-linear evolution equation are absolutely different from that of the linear evolution equation.
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    [5] Lin Wantao, Ji Zhongzhen, Wang Bin, 2001: Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 604-612.  doi: 10.1007/s00376-001-0048-7
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    [10] Yanchen ZHOU, Jiuwei ZHAO, Ruifen ZHAN, Peiyan CHEN, Zhiwei WU, Lan WANG, 2021: A Logistic-growth-equation-based Intensity Prediction Scheme for Western North Pacific Tropical Cyclones, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1750-1762.  doi: 10.1007/s00376-021-0435-1
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    [12] Chen Jiabin, Wang Jun, 1996: Studies on Non-interpolating Semi-Lagrangian Scheme and Numerical Solution to KdV Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 265-268.  doi: 10.1007/BF02656869
    [13] Jun ZHANG, Jiming SUN, Wei DENG, Wenhao HU, Yongqing WANG, 2023: The Importance of the Shape Parameter in a Bulk Parameterization Scheme to the Evolution of the Cloud Droplet Spectrum during Condensation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 155-167.  doi: 10.1007/s00376-022-2065-7
    [14] Lu YANG, Cong-Lan CHENG, Yu XIA, Min CHEN, Ming-Xuan CHEN, Han-Bin ZHANG, Xiang-Yu HUANG, 2023: Evaluation of the Added Value of Probabilistic Nowcasting Ensemble Forecasts on Regional Ensemble Forecasts, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 937-951.  doi: 10.1007/s00376-022-2056-8
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    [17] Baofeng JIAO, Lingkun RAN, Na LI, Ren CAI, Tao QU, Yushu ZHOU, 2023: Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 856-873.  doi: 10.1007/s00376-022-1435-5
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    [19] Ji Zhongzhen, Wang Bin, 1997: Multispectrum Method and the Computation of Vapor Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 563-568.  doi: 10.1007/s00376-997-0074-1
    [20] Zhao Ying, Wang Bin, Ji Zhongzhen, 2002: Symplectic-like Difference Schemes for Generalized Hamiltonian Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 719-726.  doi: 10.1007/s00376-002-0011-2
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    • Manuscript History

    Manuscript received: 10 July 2002
    Manuscript revised: 10 July 2002
    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

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    A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations

    • 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
    • Manuscript received: 2002-07-10
    • Manuscript revised: 2002-07-10

    Abstract: For several difference schemes of linear and non-linear evolution equations, taking the one-dimensional linear and non-linear advection equations as examples, a comparative analysis for computational stability is carried out and the relationship between non-linear computational stability, the construction of difference schemes, and the form of initial values is discussed. It is proved through comparative analysis and numerical experiment that the computational stability of the difference schemes of the non-linear evolution equation are absolutely different from that of the linear evolution equation.

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