A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

Mikhail A. Bochev

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    Abstract

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term $g(t)$, constructed with the help of the truncated singular value decomposition. The second stage is a special residual-based block Krylov subspace method. The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Because both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time-exact method. Numerical experiments are presented to demonstrate efficiency of the proposed method.
    Original languageUndefined
    Pages (from-to)557-574
    Number of pages18
    JournalNumerical linear algebra with applications
    Volume20
    Issue number4
    DOIs
    Publication statusPublished - 2013

    Keywords

    • EWI-23909
    • MSC-65L05
    • MSC-65L60
    • MSC-65F60
    • Block Krylov subspace methods
    • Matrix exponential
    • IR-87652
    • Exponential time integration
    • Proper orthogonal decomposition
    • Truncated SVD
    • Unconditionally stable time integration
    • METIS-300125
    • Exponential residual

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