Analytic pseudoorthogonalization methods for linear two-point boundary value problems illustrated by the Orr-Sommerfeld equation

  • Martin A. Monkewitz
Original Papers
Received:

Summary

Two pseudoorthogonalization schemes for the solution of two-point linear boundary eigenvalue problems are discussed, which serve, during numerical integration, to keep the solutions linearly independent, without disturbing their inherent analytic dependence upon parameters and initial conditions. Solutions of the Orr-Sommerfeld equation are given as examples.

Keywords

Mathematical Method Eigenvalue Problem Linear Boundary Analytic Dependence Boundary Eigenvalue 
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Zusammenfassung

Zwei Pseudoorthogonalisationsverfahren für die numerische Lösung von linearen Rand-Eigenwertproblemen werden besprochen, die die analytische Abhängigkeit der Lösungen von ihren Anfangsbedingungen und Parametern erhalten und die lineare Unabhängigkeit der Lösungen während der Integration garantieren. Lösungen der Orr-Sommerfeld Gleichung sind als Beispiele angeführt.

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References

  1. [1]
    A. R. Wazzan, T. T. Okamura andA. M. O. Smith,Spatial and Temporal Stability Charts for the Falkner-Skan Boundary Layer Profiles, Douglas Aircraft Co., Report No. DAC-67086, 1968.Google Scholar
  2. [2]
    L. Bieberbach,Theorie der gewöhnlichen Differentialgleichungen, Springer, Berlin, 1965.Google Scholar
  3. [3]
    M. R. Scott andH. A. Watts,Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization, SIAM J. Numer. Analysis14 Nr. 1 (March 1977).Google Scholar
  4. [4]
    H. Schlichting,Grenzschichttheorie, G. Braun, Karlsruhe, 1965.Google Scholar

Copyright information

© Birkhäuser-Verlag 1978

Authors and Affiliations

  • Martin A. Monkewitz
    • 1
  1. 1.Institute of AerodynamicsETH ZurichZurichSwitzerland

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