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

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Benner,  Peter
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
TU Chemnitz;

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1807.08524.pdf
(Preprint), 621KB

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Citation

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


Cite as: http://hdl.handle.net/21.11116/0000-0004-69AC-5
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.