Recent Advances in Krylov Subspace Spectral Methods
نویسنده
چکیده
This paper reviews the main properties, and most recent developments, of Krylov subspace spectral (KSS) methods for time-dependent variable-coefficient PDE. These methods use techniques developed by Golub and Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral domain in order to achieve high-order accuracy in time and stability characteristic of implicit time-stepping schemes, even though KSS methods themselves are explicit. In fact, for certain problems, 1-node KSS methods are unconditionally stable. Furthermore, these methods are equivalent to high-order operator splittings, thus offering another perspective for further analysis and enhancement.
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