Sequential regularization methods for higher index DAEs with constraint singularities: linear index-$2$ case

Uri M. Ascher, Ping Lin

    Research output: Contribution to journalArticle

    38 Citations (Scopus)

    Abstract

    Standard stabilization techniques for higher index differential-algebraic equations (DAEs) often involve elimination of the algebraic solution components. This may not work well if there are singularity points where the constraint Jacobian matrix becomes rank deficient. This paper proposes instead a sequential regularization method (SRM)—a functional iteration procedure for solving problems with isolated singularities which have smooth differential solution components.For linear index-2 DAEs we consider both initial value problems (IVPs) and boundary value problems (BVPs). The convergence of the SRM is described and proved in detail. We believe that this is the first convergence proof for any method for DAEs with this type of constraint singularities. Moreover, the regularization parameter in our method is not necessarily very small, so the SRM is an important improvement over usual regularization methods. Various aspects of the subsequent numerical discretization of the regularized problems are discussed as well and some numerical verifications are carried out.
    Original languageEnglish
    Pages (from-to)1921-1940
    Number of pages20
    JournalSIAM Journal on Numerical Analysis
    Volume33
    Issue number5
    DOIs
    Publication statusPublished - 1996

    Keywords

    • Differential-algebraic equations
    • Sequential regularization method

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