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Krylov subspace approximations for the exponential Euler method : error estimates and the harmonic Ritz approximant

Carr, Elliot Joseph, Turner, Ian, & Ilic, Milos (2011) Krylov subspace approximations for the exponential Euler method : error estimates and the harmonic Ritz approximant. In McLean, W. & Roberts, A.J. (Eds.) Proceedings of the 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, ANZIAM Journal, University of New South Wales, Sydney, NSW, C612-C627.

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Abstract

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

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ID Code: 44070
Item Type: Conference Paper
Keywords: Krylov subspace methods, Matrix function approximation, Exponential integrators, Phi function, Arnoldi Method, Error estimates
ISSN: 1446-8735
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2011 Austral, Mathematical Society
Deposited On: 19 Aug 2011 09:46
Last Modified: 20 Aug 2011 19:10

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