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21277 A block Krylov subspace time-exact solution method for linear ODE systems
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Botchev, M.A. (2012) A block Krylov subspace time-exact solution method for linear ODE systems. Memorandum 1973, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850

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We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term $g(t)$, constructed with the help of the truncated SVD (singular value decomposition). The second stage is a special residual-based block Krylov subspace method.
The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Since both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time-exact method. Numerical experiments are presented to demonstrate efficiency of the new method, as compared to an exponential time integrator with Krylov subspace matrix function evaluations.

Item Type:Internal Report (Memorandum)
Research Group:EWI-MACS: Mathematics of Computational Science
Additional Information:The author's surname can also be spelled as "Bochev"
Uncontrolled Keywords:Block Krylov subspace methods, Matrix exponential, Exponential time integration, Unconditionally stable time integration, Exponential residual, Truncated SVD, Proper orthogonal decomposition
ID Code:21277
Deposited On:17 January 2012
More Information:statisticsmetis

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