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

Peter Benner; Norman Lang

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arXiv · 1807.08524

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

Peter Benner·Norman Lang

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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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Peter Benner, Norman Lang. 2018-07-23. Peer Methods for the Solution of Large-Scale Differential Matrix Equations. https://arxiv.org/abs/1807.08524

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