English

Dense output for strong stability preserving Runge-Kutta methods

Numerical Analysis 2016-11-16 v2

Abstract

We investigate dense output formulae (also known as continuous extensions) for strong stability preserving (SSP) Runge-Kutta methods. We require that the dense output formula also possess the SSP property, ideally under the same step-size restriction as the method itself. A general recipe for first-order SSP dense output formulae for SSP methods is given, and second-order dense output formulae for several optimal SSP methods are developed. It is shown that SSP dense output formulae of order 3 and higher do not exist, and that in any method possessing a second-order SSP dense output, the coefficient matrix A has a zero row.

Keywords

Cite

@article{arxiv.1605.02429,
  title  = {Dense output for strong stability preserving Runge-Kutta methods},
  author = {David I. Ketcheson and Lajos Lóczi and Aliya Jangabylova and Adil Kusmanov},
  journal= {arXiv preprint arXiv:1605.02429},
  year   = {2016}
}
R2 v1 2026-06-22T13:56:00.660Z