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  Peer Methods for the Solution of Large-Scale Differential Matrix Equations

Benner, P., & Lang, N. (in preparation). Peer Methods for the Solution of Large-Scale Differential Matrix Equations.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0004-69AC-5 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-69AD-4
Genre: Paper

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1807.08524.pdf (Preprint), 621KB
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 Creators:
Benner, Peter1, 2, Author              
Lang, Norman2, Author
Affiliations:
1Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738141              
2TU Chemnitz, ou_persistent22              

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Free keywords: Mathematics, Numerical Analysis, math.NA,
 Abstract: We consider the application of implicit and linearly implicit (Rosenbrock-type) peer methods to matrix-valued ordinary differential equations. In particular the differential Riccati equation (DRE) is investigated. For the Rosenbrock-type schemes, a reformulation capable of avoiding a number of Jacobian applications is developed that, in the autonomous case, reduces the computational complexity of the algorithms. Dealing with large-scale problems, an efficient implementation based on low-rank symmetric indefinite factorizations is presented. The performance of both peer approaches up to order 4 is compared to existing implicit time integration schemes for matrix-valued differential equations.

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 Dates: 2018-07-23
 Publication Status: Not specified
 Pages: 29 pages, 2 figures (including 6 subfigures each), 3 tables, Corrected typos
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1807.08524
URI: http://arxiv.org/abs/1807.08524
 Degree: -

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