Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems

Hendrik Ranocha; David I. Ketcheson

doi:10.1137/19m1290346

Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems

Hendrik Ranocha, David I. Ketcheson

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Many important initial value problems have the property that energy is nonincreasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge--Kutta methods for nonlinear or nonautonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed, and an example is given in which unconditional energy stability is obtained with an explicit scheme.

Original language	English (US)
Pages (from-to)	3382-3405
Number of pages	24
Journal	SIAM Journal on Numerical Analysis
Volume	58
Issue number	6
DOIs	https://doi.org/10.1137/19m1290346
State	Published - Nov 24 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-12-08
Acknowledgements: Research reported in this publication was supported by the King Abdullah University of Scienceand Technology (KAUST). The first author was partially supported by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) under Grant SO 363/14-1.

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https://repository.kaust.edu.sa/bitstream/10754/659989/3/energy%20stability.pdf

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title = "Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems",

abstract = "Many important initial value problems have the property that energy is nonincreasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge--Kutta methods for nonlinear or nonautonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed, and an example is given in which unconditional energy stability is obtained with an explicit scheme.",

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note = "KAUST Repository Item: Exported on 2020-12-08 Acknowledgements: Research reported in this publication was supported by the King Abdullah University of Scienceand Technology (KAUST). The first author was partially supported by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) under Grant SO 363/14-1.",

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AU - Ranocha, Hendrik

AU - Ketcheson, David I.

N1 - KAUST Repository Item: Exported on 2020-12-08 Acknowledgements: Research reported in this publication was supported by the King Abdullah University of Scienceand Technology (KAUST). The first author was partially supported by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) under Grant SO 363/14-1.

PY - 2020/11/24

Y1 - 2020/11/24

N2 - Many important initial value problems have the property that energy is nonincreasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge--Kutta methods for nonlinear or nonautonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed, and an example is given in which unconditional energy stability is obtained with an explicit scheme.

AB - Many important initial value problems have the property that energy is nonincreasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge--Kutta methods for nonlinear or nonautonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed, and an example is given in which unconditional energy stability is obtained with an explicit scheme.

UR - http://hdl.handle.net/10754/659989

UR - https://epubs.siam.org/doi/10.1137/19M1290346

U2 - 10.1137/19m1290346

DO - 10.1137/19m1290346

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VL - 58

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EP - 3405

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems

Abstract

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