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On the stability regions of multistep multiderivative methods

Part of the Lecture Notes in Mathematics book series (LNM,volume 631)

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References

  1. Ahlfors, L.V., Complex Analysis, McGraw-Hill, New York, 1953.

    MATH  Google Scholar 

  2. Ansell, H.G., On certain two-variable generalizations of circuit theory, with applications to networks of transmission lines and lumped reactances, IEEE Trans. on C.T. 11, (1964), 214–223.

    Google Scholar 

  3. Bickart, T.A., D.A. Burgess and H.M. Sloate, High order A-stable composite multistep methods for numerical integration of stiff differential equations, in Proc. 9th Annual Allerton Conf. on Circuit and System Theory, (1971), 465–473.

    Google Scholar 

  4. Dahlquist, G., Convergence and stability in the numerical integration of ordinary differential equations, Trans. Roy. Inst. Tech., Stockholm, Nr. 130, 1959.

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Daniel, J.W. and R.E. Moore, Computation and theory in ordinary differential equations, Freeman and Co., San Francisco, 1970.

    MATH  Google Scholar 

  7. Ehle, B.L., High order A-stable methods for the numerical solution of systems of D.E.’s, BIT 8, (1968), 276–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Genin, Y., An algebraic approach to A-stable linear multistep-multiderivative integration formulas, BIT 14, (1974), 382–406.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Griepentrog, E., Mehrschrittverfahren zur numerischen Integration von gewöhnlichen Differentialgleichungssystemen und asymptotische Exaktheit, Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe, v. 19, (1970), 637–653.

    MathSciNet  MATH  Google Scholar 

  10. Henrici, P., Discrete variable methods in ordinary differential equations, Wiley, New York, 1962.

    MATH  Google Scholar 

  11. Jeltsch, R., Integration of iterated integrals by multistep methods, Numer. Math. 21, (1973), 303–316.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Jeltsch, R., A necessary condition for A-stability of multistep multiderivative methods, to appear in Math. Comp., 30 (1976).

    Google Scholar 

  13. Jeltsch, R., Stiff stability of multistep multiderivative methods, to appear in SIAM J. on numer. Anal.

    Google Scholar 

  14. Jeltsch, R., Multistep multiderivative methods for the numerical solution of initial value problems of ordinary differential equations., Seminar Notes 1975/76, University of Kentucky, 1976.

    Google Scholar 

  15. Nevanlinna, O. and A.H. Sipilä, A nonexistence theorem for explicit A-stable methods, Math. Comp., 28 (1974), 1053–1055.

    MathSciNet  MATH  Google Scholar 

  16. Reimer, M., Finite difference forms containing derivatives of higher order, SIAM J. Numer. Anal., 5 (1968), 725–738.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Rubin, W.B., A-stability and composite multistep methods, Ph. D. Thesis, EE Dept., Syracuse University, New York, 1973.

    Google Scholar 

  18. Sloate, H.M. and T.A. Bickart, A-stable composite multistep methods, JACM 20, (1973), 7–26.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Stetter, H.J., Analysis of discretization methods of ordinary differential equations, Springer, New York, 1973.

    CrossRef  MATH  Google Scholar 

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© 1978 Springer-Verlag

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Jeltsch, R. (1978). On the stability regions of multistep multiderivative methods. In: Bulirsch, R., Grigorieff, R.D., Schröder, J. (eds) Numerical Treatment of Differential Equations. Lecture Notes in Mathematics, vol 631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067464

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  • DOI: https://doi.org/10.1007/BFb0067464

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