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Remarks on Picard-Lindelöf iteration

Part II

  • Part II Numerical Mathematics
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References

  1. W. H. Beyer ed.:CRC Standard Mathematical Tables, CRC Press, Inc., Boca Ration, 27th Edition, 1986.

    Google Scholar 

  2. G. Dahlquist:G-stability is equivalent to A-stability, BIT18 (1978), 384–401.

    Article  Google Scholar 

  3. I. S. Gradshteyn, I. M. Ryzhik:Table of Integrals, Series and Products. English edition. Scripta Technica, Inc. New York, London, 1965.

    Google Scholar 

  4. E. Hairer, S. P. Nørsett, G. Wanner:Solving Ordinary Differential Equations I, Springer-Verlag, Berlin-Heidelberg, 1987.

    Google Scholar 

  5. P. Henrici:Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons, Inc., New York-London-Sydney, 1962.

    Google Scholar 

  6. E. Lelarasmee, A. E. Ruehli, A. L. Sangiovanni-Vincentelli:The waveform relaxation methods for time-domain analysis of large scale integrated circuits, IEEE Trans. On CAD of IC and Syst.,1, 3 (1982), 131–145.

    Google Scholar 

  7. R. J. LeVeque, L. N. Trefethen:On the resolvent condition in the Kreiss matrix theorem, BIT24, (1984), 584–591.

    Article  Google Scholar 

  8. E. Lindelöf: Sur l'application des méthodes d'approximations successives à l'étude des intégrales réelles des équations differentielles ordinaires, J. de Math. Pures et Appl, 4e série,10 (1894), 117–128.

    Google Scholar 

  9. Ch. Lubich, A. Ostermann:Multigrid dynamic iteration for parabolic equations, BIT 27 (1987), 216–234.

    Article  Google Scholar 

  10. U. Miekkala:Dynamic iteration methods applied to linear DAE systems, Helsinki University of Technology, Report-Mat-A252 (1987).

  11. U. Miekkala, O. Nevanlinna:Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput.,8 (1987), 459–482.

    Article  Google Scholar 

  12. U. Miekkala, O. Nevanlinna:Sets of convergence and stability regions, BIT27 (1987), 554–584.

    Article  Google Scholar 

  13. W. E. Milne:Numerical Solution of Differential Equations, John Wiley & Sons, Inc., London 1953.

    Google Scholar 

  14. D. Mitra:Asynchronous relaxations for the numerical solution of differential equations by parallel processors, SIAM J. Sci. Stat. Comput.8 (1987), s43-s58.

    Article  Google Scholar 

  15. O. Nevanlinna, F. Odeh:Remarks on the convergence of waveform relaxation method, Numer. Funct. Anal. Optimiz.,9 (1987), 435–445.

    Google Scholar 

  16. E. Picard: Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires, J. de Math. Pures et Appl. 4e série,9 (1893), 217–271.

    Google Scholar 

  17. J. White, F. Odeh, A. S. Vincentelli, A. Ruehli:Waveform relaxation: theory and practice, UC Berkeley, Memorandum No UCB/ERL M85/65 (1985).

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Authors and Affiliations

  1. Institute of Mathematics, Helsinki University of Technology, SF-02150, Espoo, Finland

    Olavi Nevanlinna

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  1. Olavi Nevanlinna
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The first part of this paper was published in BIT 29 (1988), pp. 328–346.

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Nevanlinna, O. Remarks on Picard-Lindelöf iteration. BIT 29, 535–562 (1989). https://doi.org/10.1007/BF02219239

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  • DOI: https://doi.org/10.1007/BF02219239

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