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


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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Manuscript History

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

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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