Volume 20, pp. 212-234, 2005.

Krylov subspace spectral methods for variable-coefficient initial-boundary value problems

James V. Lambers


This paper presents an alternative approach to the solution of diffusion problems in the variable-coefficient case that leads to a new numerical method, called a Krylov subspace spectral method. The basic idea behind the method is to use Gaussian quadrature in the spectral domain to compute components of the solution, rather than in the spatial domain as in traditional spectral methods. For each component, a different approximation of the solution operator by a restriction to a low-dimensional Krylov subspace is employed, and each approximation is optimal in some sense for computing the corresponding component. This strategy allows accurate resolution of all desired frequency components without having to resort to smoothing techniques to ensure stability.

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Key words

spectral methods, Gaussian quadrature, variable-coefficient, Lanczos method

AMS subject classifications

65M12, 65M70, 65D32

ETNA articles which cite this article

Vol. 28 (2007-2008), pp. 114-135 James V. Lambers: Derivation of high-order spectral methods for time-dependent PDE using modified moments
Vol. 31 (2008), pp. 86-109 James V. Lambers: Enhancement of Krylov subspace spectral methods by block Lanczos iteration

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