Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
KAUST Grant NumberFIC/2010/05-2000000231
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AbstractPerturbed 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.
CitationHigueras I, Ketcheson DI, Kocsis TA (2018) Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-018-0664-3.
SponsorsMinisterio de Economía y Competitividad[MTM2016-77735-C3-2-P, MTM2014-53178-P]
King Abdullah University of Science and Technology[FIC/2010/05-2000000231]
JournalJournal of Scientific Computing