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Ordinary Papers

On conditions for the existence and uniqueness of solutions to the algebraic equations in Runge-Kutta methods

  • Part II Numerical Mathematics
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Abstract

This paper deals with the systems of algebraic equations arising in the application of implicit Runge-Kutta methods.

Equivalent conditions under which three wide classes of differential equations have unique solutions are presented. In addition, sufficient conditions for their existence are given.

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References

  1. J. C. Butcher,Implicit Runge-Kutta processes, Math. Comp. 18 (1964), 50–64.

    Google Scholar 

  2. M. Crouzeix, W. H. Hundsdorfer and M. N. Spijker,On the existence of solutions to the algebraic equations in implicit Runge-Kutta Methods, BIT 23 (1983) 84–91.

    Google Scholar 

  3. G. Dahlquist and R. Jeltsch,Generalized disks of contractivity for explicit and implicit Runge-Kutta methods, Report TRITA-NA-7906 Dept. Comp. Sci., Roy. Inst. of Techn.; Stockholm (1979).

  4. G. Di Lena and G. Piazza,Una classe di metodi Runge-Kutta con esistenza dei parametri implicitamente definiti, Pubblicazioni I.A.C. Serie III n. 201 (1981).

  5. W. H. Hundsdorfer and M. N. Spijker,A note on B-stability of Runge-Kutta methods, Numer. Math. 36, (1981) 319–331.

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  6. J. M. Ortega and W. C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables, New York A. P. (1970).

  7. F. Reinhard, J. Schneid and C. W. Ueberhuber,Order results for implicit Runge-Kutta methods applied to stiff systems. Institut für Angewandte und Numerische Mathematik, Wien Nr. 53/82.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bari, Via Nicolai, 2, 70100, BARI, Italy

    Giovanni Di Lena & Roberto I. Peluso

Authors
  1. Giovanni Di Lena
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  2. Roberto I. Peluso
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Di Lena, G., Peluso, R.I. Ordinary Papers. BIT 25, 223–232 (1985). https://doi.org/10.1007/BF01934999

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  • DOI: https://doi.org/10.1007/BF01934999

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