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Global accuracy and A-stability of one- and two-step integration formulae for stiff ordinary differential equations

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Conference on the Numerical Solution of Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 109))

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References

  1. C. F. Curtiss and J. O. Hirschfelder, "Integration of stiff equations," Proc. Natl. Acad. Sci., USA 38 (1952) 235–243.

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  2. G. G. Dahlquist, "A special stability criterion for linear multistep methods," BIT 3 (1963) 22–43.

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  3. W. Liniger and R. A. Willoughby, "Efficient integration methods for stiff systems of ordinary differential equations," IBM Research Report RC 1970 (December 1967).

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  4. E. Stiefel, Einfuehrung in die numerische Mathematik, 2d. ed., Teubner, Stuttgart (1963) p. 158.

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  5. G. G. Dahlquist, "A numerical method for some ordinary differential equations with large Lipschitz constants," Proc. IFIPS Congress, Edinburgh (August 1968).

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  6. W. Liniger, "Global accuracy and A-stability of one-and two-step integration formulae for stiff ordinary differential equations," IBM Research Report RC 2396 (March 1969).

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  7. C. W. Gear, "The automatic integration of stiff ordinary differential equations," Proc. IFIPS Congress, Edinburgh (August 1968) A81–85.

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

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  9. W. Liniger, "Zur Stabilitaet der numerischen Integrationsmethoden fuer Differentialgleichungen," Doctoral Thesis, University of Lausanne (1957).

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Authors
  1. W. Liniger
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J. Li. Morris

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© 1969 Springer-Verlag

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Liniger, W. (1969). Global accuracy and A-stability of one- and two-step integration formulae for stiff ordinary differential equations. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060027

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  • DOI: https://doi.org/10.1007/BFb0060027

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04628-8

  • Online ISBN: 978-3-540-36158-9

  • eBook Packages: Springer Book Archive

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