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Local structure-preserving algorithms for partial differential equations

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Abstract

In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations, which are the natural generalization of the corresponding global SPAs. Local SPAs for the problems with proper boundary conditions are global SPAs, but the inverse is not necessarily valid. The concept of the local SPAs can explain the difference between different SPAs and provide a basic theory for analyzing and constructing high performance SPAs. Furthermore, it enlarges the applicable scopes of SPAs. We also discuss the application and the construction of local SPAs and derive several new SPAs for the nonlinear Klein-Gordon equation.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China

    YuShun Wang

  2. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

    YuShun Wang & Bin Wang

  3. Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, 100871, China

    MengZhao Qin

Authors
  1. YuShun Wang
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  2. Bin Wang
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  3. MengZhao Qin
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Corresponding author

Correspondence to YuShun Wang.

Additional information

This work was supported by the National Basic Research Program (Grant No. 2005CB321703). The first author was supported by the National Natural Science Foundation of China (Grant Nos. 40405019, 10471067) and the Major Research Projects of Jiangsu Province (Grant No. BK2006725); the second author was supported by the National Natural Science Foundation of China (Innovation Group) (Grant No. 40221503) and the third author was supported by the National Natural Science Foundation of China (Grant No. 10471145)

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Wang, Y., Wang, B. & Qin, M. Local structure-preserving algorithms for partial differential equations. Sci. China Ser. A-Math. 51, 2115–2136 (2008). https://doi.org/10.1007/s11425-008-0046-7

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  • DOI: https://doi.org/10.1007/s11425-008-0046-7

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