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On the choice of an appropriate imbedding algorithm for the solution of unstable linear boundary value problems

Zur Wahl eines geeigneten Einbettungsalgorithmus bei der Lösung instabiler linearer Randwertprobleme

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Abstract

The method of Extended (or Generalized) Invariant Imbedding solves unstable linear boundary value problems in a stable manner. The method requires the integration of one of four different matrix Riccati differential equations (four different algorithms). In this contribution the questions of existence, stability, boundedness and error propagation of these Riccati equations are discussed in order to help the user to choose the appropriate algorithm.

Zusammenfassung

Das Verfahren des Erweiterten (oder Verallgemeinerten) Invarianten Einbettens kann instabile lineare Randwertaufgaben “stabil” lösen. Das Verfahren erfordert die Integration von einer von vier verschiedenen Matrixdifferentialgleichungen des Riccati-Typs (vier verschiedene numerische Algorithmen). Dieser Beitrag behandelt die Frage nach Existenz, Stabilität, Beschränktheit und Fehlerfortpflanzung dieser Riccatigleichung um die Auswahl des geeigneten Algorithmus zu erleichtern.

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References

  1. Bramley, J. S.: The numerical solution of unstable ordinary differential equations. Appl. Math. Comput.4, 307–316 (1978).

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  2. Breitenecker, F.: Extended invariant imbedding for the solution of unstable linear boundary value problems. Thesis, Technical University Vienna, 1979 (in German).

  3. Breitenecker, F.: On the solution of linear boundary value problems by extended invariant imbedding. Computing28, 333–343 (1982).

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  4. Breitenecker, F.: Invariant imbedding and multiple shooting for the solution of unstable linear boundary value problems. Appl. Math. Comput.9, 235–244 (1981).

    Article  Google Scholar 

  5. Breitenecker, F.: Generalized invariant imbedding for the solution of unstable linear boundary value problems. (To appear.)

  6. Jakobson, D. H.: New conditions for boundedness of the solution of a matrix Riccati differential equation. J. Diff. Equ.8, 258–263 (1970).

    Article  Google Scholar 

  7. Meyer, G. H.: On a generalized theory of characteristics and the method of invariant imbedding. SIAM J. Appl. Math.16, 488–503 (1968).

    Article  Google Scholar 

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  1. Institut für Technische Mathematik, Technische Universität Wien, Gusshausstrasse 27-29, A-1040, Wien, Austria

    F. Breitenecker

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  1. F. Breitenecker
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Breitenecker, F. On the choice of an appropriate imbedding algorithm for the solution of unstable linear boundary value problems. Computing 31, 173–176 (1983). https://doi.org/10.1007/BF02259912

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  • DOI: https://doi.org/10.1007/BF02259912

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