Stability control for approximate implicit time-stepping schemes with minimal residual iterations

Mikhail A. Bochev, G.L.G. Sleijpen, H.A. van der Vorst

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    Abstract

    Implicit schemes for the integration of ODEs are popular when stability is more of concern than accuracy, for instance for the computation of a steady state solution. However, in particular for very large systems, the solution of the linear systems involved may be very expensive. When these systems are solved iteratively to a certain tolerance, it is often not known which tolerance has to be taken. We propose a different strategy, where the number of iterations is fixed, but the step size is controlled with respect to stability. Numerical tests show the effectiveness of this approach in comparison with an implicit scheme that iterates to a certain tolerance.
    Original languageUndefined
    Article number10.1016/S0168-9274(98)00138-X
    Pages (from-to)239-253
    Number of pages15
    JournalApplied numerical mathematics
    Volume31
    Issue number3
    DOIs
    Publication statusPublished - 1999

    Keywords

    • IR-66812
    • EWI-8890
    • MSC-65L20

    Cite this

    Bochev, M. A., Sleijpen, G. L. G., & van der Vorst, H. A. (1999). Stability control for approximate implicit time-stepping schemes with minimal residual iterations. Applied numerical mathematics, 31(3), 239-253. [10.1016/S0168-9274(98)00138-X]. https://doi.org/10.1016/S0168-9274(98)00138-X