Numerical Methods for Initial-Boundary-Value Problems for First Order Quasilinear Hyperbolic Systems in Two Independent Variables

  • Zhu You-lan
  • Chen Bing-mu
  • Zhong Xi-chang
  • Zhang Zuo-min

Abstract

When discussing numerical methods for hyperbolic systems, it is usual to construct difference schemes and do theoretical analysis only for pure initial-value problems. However, most of the problems which exist in practice are initial-boundary-value problems. When applying the results from the pure initial-value problems (PIVP) to the initial-boundary-value problems (IBVP), difficulties are encountered since we usually do not know how to calculate the bounday points and how to ascertain whether an algorithm for boundary points is reasonable.

Keywords

Assure Cond Estima Bove 

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References

  1. [1]
    Rusanov, V. V., On the stability of block-double-sweep methods, Symposium Mathema-tics of Computation, No. 6, The Academy of Sciences of USSB, Moscow, 1960 (in Russian).Google Scholar
  2. [2]
    Gelfand, I. M. and Lokutsieuski, O. V., The double sweep method for solution of difference equations, appendix II of book [6].Google Scholar
  3. [3]
    Zhu, Youlan, A numerical method for a class of initial-boundary-value problems of first order quasilinear hyperbolic systems with three independent variables, Technical Report of The Institute of Computing Technology, The Chinese Academy of Sciences, Beijing, 1973 (inChinese).Google Scholar
  4. [4]
    Rusanov, V. V., On solution of difference equations, Report of Academy of Sciences of USSR, 136 (1961), No. 1, 33–35 (in Russian). 160 1 Methods for IBVP in Two Independent VariablesGoogle Scholar
  5. [5]
    Gantmacher, F. B., The theory of matrices, Chelsea Publishing Co., New York, N. Y., 1959.MATHGoogle Scholar
  6. [6]
    Godunov, S. K. and Byabenki, V. S., Theory of difference schemes-an introduction, North-Holland, Amsterdam and Interscience-Wiley, New York, 1964.MATHGoogle Scholar
  7. [1]
    Zhu Youlan, et al., Difference schemes for initial-boundary-value problems of hyperbolic systems and examples of application, Scientia Sinica, 1979, Special Issue (II), 261–280 (English Edition).Google Scholar
  8. [2]
    Zhu Youlan, Difference schemes for initial-boundary-value problems for first order hyperbolic systems and their stability, Mathematicae Numericae Sinica, 1979, No. 1, 1–30.Google Scholar
  9. [3]
    Richtmyer, R. D. and Morton, K. W., Difference methods for initial-value problems, Second Edition, Wiley, New York, 1967.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Zhu You-lan
    • 1
  • Chen Bing-mu
    • 1
  • Zhong Xi-chang
    • 1
  • Zhang Zuo-min
    • 1
  1. 1.Computing CenterChinese Academy of SciencesBeijingThe People’s Republic of China

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