Performance assessment of exponential Rosenbrock method for large systems of ODE

Carr, Elliot Joseph, Moroney, Timothy J., & Turner, Ian (2012) Performance assessment of exponential Rosenbrock method for large systems of ODE. ANZIAM Journal, 54, C102-C118.

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Abstract

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

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ID Code: 54569
Item Type: Journal Article
Refereed: Yes
ISSN: 1446-8735
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Australian Mathematical Society
Deposited On: 05 Nov 2012 02:36
Last Modified: 05 May 2016 03:04

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