Document Type
Conference Paper
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
Abstract
The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) class of explicit schemes for the integration of large systems of PDEs with diffusive terms is presented. FRKC2 schemes are straightforward to implement through ordered sequences of forward Euler steps with complex stepsizes, and easily parallelised for large scale problems on distributed architectures.
Preserving 7 digits for accuracy at 16 digit precision, the schemes are theoretically capable of maintaining internal stability at acceleration factors in excess of 6000 with respect to standard explicit Runge-Kutta methods. The stability domains have approximately the same extents as those of RKC schemes, and are a third longer than those of RKL2 schemes. Extension of FRKC methods to fourth-order, by both complex splitting and Butcher composition techniques, is discussed.
A publicly available implementation of the FRKC2 class of schemes may be obtained from maths.dit.ie/frkc
DOI
https://doi.org/10.21427/D7J039
Recommended Citation
O'Sullivan, S. (2016) Factorized Runge-Kutta-Chebyshev Methods. Astronum 2016 - 11th Annual International Conference on Numerical Modeling of Space Plasma Flows, June 6-10, 2016. doi:10.21427/D7J039
Included in
Astrophysics and Astronomy Commons, Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons
Publication Details
Astronum 2016 - 11th Annual International Conference on Numerical Modeling of Space Plasma Flows, June 6-10, 2016.