Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

Inmaculada Higueras*, David I. Ketcheson, Tihamér A. Kocsis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.

Original languageEnglish (US)
Pages (from-to)1337-1369
Number of pages33
JournalJournal of Scientific Computing
Volume76
Issue number3
DOIs
StatePublished - Sep 1 2018

Keywords

  • Monotonicity
  • Runge–Kutta methods
  • Strong stability preserving
  • Time discretization

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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