A Broyden rank p+1 update continuation method with subspace iteration

T.L. Noorden, van, S.M. Verduyn Lunel, A. Bliek

    Research output: Contribution to journalArticleAcademicpeer-review

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    Abstract

    In this paper we present an efficient branch-following procedure that can be used not only to compute branches of periodic solutions of periodically forced dynamical systems but also to determine the stability of the periodic solutions. The procedure combines Broyden's method with a subspace iteration method to determine the dominant eigenvalues. The method has connections with the hybrid Newton--Picard methods developed by Lust et al. in [SIAM J. Sci. Comput., 19 (1998) pp. 1188--1209]. A convergence analysis of the procedure is presented. The method is applied to the computation of periodic states of a reverse flow reactor, and its performance is compared with two variants of the hybrid Newton--Picard method.
    Original languageEnglish
    Pages (from-to)1921-1940
    JournalSIAM Journal on Scientific Computing
    Volume25
    Issue number6
    DOIs
    Publication statusPublished - 2004

    Fingerprint

    P-rank
    Continuation Method
    Newton-Raphson method
    Update
    Subspace
    Iteration
    Periodic Solution
    Dynamical systems
    Branch
    Broyden's Method
    Subspace Methods
    Iteration Method
    Convergence Analysis
    Reactor
    Reverse
    Dynamical system
    Eigenvalue

    Cite this

    Noorden, van, T.L. ; Verduyn Lunel, S.M. ; Bliek, A. / A Broyden rank p+1 update continuation method with subspace iteration. In: SIAM Journal on Scientific Computing. 2004 ; Vol. 25, No. 6. pp. 1921-1940.
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    A Broyden rank p+1 update continuation method with subspace iteration. / Noorden, van, T.L.; Verduyn Lunel, S.M.; Bliek, A.

    In: SIAM Journal on Scientific Computing, Vol. 25, No. 6, 2004, p. 1921-1940.

    Research output: Contribution to journalArticleAcademicpeer-review

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    T1 - A Broyden rank p+1 update continuation method with subspace iteration

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    AU - Verduyn Lunel, S.M.

    AU - Bliek, A.

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