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

  • Inmaculada Higueras
  • David I. Ketcheson
  • Tihamér A. Kocsis


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.


Strong stability preserving Monotonicity Runge–Kutta methods Time discretization 

Mathematics Subject Classification

65L06 65L20 65M20 


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Authors and Affiliations

  1. 1.Public University of NavarrePamplonaSpain
  2. 2.King Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  3. 3.Széchenyi István UniversityGyőrHungary

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