Abstract.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.

Received: August 14, 2008

AMS Subject Classification: 65M12, 65M70, 65D32

Key Words and Phrases: spectral methods, Gaussian quadrature, variable-coefficient, Lanczos method, stability, heat equation, wave equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 2