2019/10/06 by Paul Tranquilli, Tranquilli, Paul, Ross Glandon +3
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Matrix Theory and Algorithms #Numerical methods for differential equations #cs.NA #math.NA #msc:65L05
paper · pdf · doi:10.48550/arxiv.1910.02514
arxiv created 2019/10/06 · arxiv updated 2019/10/08
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work proposes an extension of Rosenbrock-Krylov methods to address stability questions which arise for methods making use of inexact linear system solution strategies. Two approaches for improving the stability and efficiency of Rosenbrock-Krylov methods are proposed, one through direct control of linear system residuals and the second through a novel extension of the underlying Krylov space to include stage right hand side vectors. Rosenbrock-Krylov methods employing the new approaches show a substantial improvement in computational efficiency relative to prior implementations.