Optimal monotonicity-preserving perturbations of a given Runge–Kutta method

Date

2018

Authors

Ketcheson, David I.
Kocsis, Tihamér A.

Director

Publisher

Springer
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

  • MINECO//MTM2014-53178-P/ES/ recolecta
  • ES/1PE/MTM2016-77735/
Impacto

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.

Description

Keywords

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

Department

Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza

Faculty/School

Degree

Doctorate program

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