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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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