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

2018/07/23 by Benner, Peter, Lang, Norman
#15A23 #34A09 #65L99 #93A15 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1807.08524

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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