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Some aspects of the boundary locus method

  • Part II Numerical Mathematics
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Abstract

The boundary locus method for determining the stability region of a linear multistep method is considered from several viewpoints. In particular we show how it is related to the order of the method. These ideas are extended to Runge-Kutta and other methods.

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References

  1. L. V. Ahlfors,Complex Analysis, McGraw-Hill (1953).

  2. J. C. Butcher,A class of implicit methods for ordinary differential equations, Proceedings of the Dundee Conference on Numerical Analysis (Lecture Notes in Mathematics 506) Springer-Verlag (1975), 28–37.

  3. G. Dahlquist,A special stability problem for linear multistep methods, BIT 3 (1963), 27–43.

    Google Scholar 

  4. J. Dieudonné,Foundations of Modern Analysis, Academic Press (1960).

  5. A. Goetz,Introduction to Differential Geometry, Addison-Wesley (1970).

  6. P. K. Henrici,Discrete Variable Methods in Ordinary Differential Equations, Wiley (1962).

  7. R. Jeltsch,A necessary condition for A-stability of multistep multiderivative methods, Math. Comp. 30 (1976), 739–746.

    Google Scholar 

  8. J. D. Lambert,Computational Methods in Ordinary Differential Equations, Wiley (1973).

  9. W. Liniger,A criterion for A-stability of linear multistep integration formulae, Computing 3 (1968), 280–285.

    Google Scholar 

  10. S. P. Nørsett,A criterion for A(α)-stability of linear multistep methods, BIT 9 (1969), 259–263.

    Google Scholar 

  11. S. P. Nørsett,One-step methods of Hermite type for numerical integration of stiff systems, BIT 14 (1974), 63–77.

    Google Scholar 

  12. J. L. Siemieniuch,Properties of certain rational approximations to e −z, BIT 16 (1976), 172–191.

    Google Scholar 

  13. G. Wanner, E. Hairer and S. P. Nørsett,Order stars and stability theorems, BIT 18 (1978), 475–489.

    Google Scholar 

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Sanz-Serna, J.M. Some aspects of the boundary locus method. BIT 20, 97–101 (1980). https://doi.org/10.1007/BF01933590

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  • DOI: https://doi.org/10.1007/BF01933590

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