Implicitly Defined High-Order Operator Splittings for Parabolic and Hyperbolic Variable-Coefficient PDE Using Modified Moments
نویسنده
چکیده
This paper presents a reformulation of Krylov Subspace Spectral (KSS) Methods, which use Gaussian quadrature in the spectral domain compute high-order accurate approximate solutions to variable-coefficient time-dependent PDE. This reformulation reveals that KSS methods are actually high-order operator splittings that are defined implicitly, in terms of derivatives of the nodes and weights of Gaussian quadrature rules with respect to a parameter. We discuss the application of these modified KSS methods to parabolic and hyperbolic PDE, as well as systems of coupled PDE.
منابع مشابه
Derivation of High-order Spectral Methods for Time-dependent Pde Using Modified Moments∗
Abstract. This paper presents a reformulation of Krylov Subspace Spectral (KSS) Methods, which build on Gene Golub’s many contributions pertaining to moments and Gaussian quadrature, to produce high-order accurate approximate solutions to variable-coefficient time-dependent PDE. This reformulation serves two useful purposes. First, it more clearly illustrates the distinction between KSS methods...
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