research-article

Strong Stability of Explicit Runge--Kutta Time Discretizations

Authors:

Chi-wang ShuAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 57, Issue 3

Pages 1158 - 1182

https://doi.org/10.1137/18M122892X

Published: 01 January 2019 Publication History

Abstract

Motivated by studies on fully discrete numerical schemes for linear hyperbolic conservation laws, we present a framework on analyzing the strong stability of explicit Runge--Kutta (RK) time discretizations for seminegative autonomous linear systems. The analysis is based on the energy method and can be performed with the aid of a computer. Strong stability of various RK methods, including a sixteen-stage embedded pair of order nine and eight, has been examined under this framework. Based on numerous numerical observations, we further characterize the features of strongly stable schemes. A both necessary and sufficient condition is given for the strong stability of RK methods of odd linear order.

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Cited By

Xu YShu CZhang Q(2024)Stability Analysis and Error Estimate of the Explicit Single-Step Time-Marching Discontinuous Galerkin Methods with Stage-Dependent Numerical Flux Parameters for a Linear Hyperbolic Equation in One DimensionJournal of Scientific Computing10.1007/s10915-024-02621-2100:3Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1007/s10915-024-02621-2
Sun ZXing Y(2023)On Generalized Gauss–Radau Projections and Optimal Error Estimates of Upwind-Biased DG Methods for the Linear Advection Equation on Special Simplex MeshesJournal of Scientific Computing10.1007/s10915-023-02166-w95:2Online publication date: 18-Mar-2023
https://dl.acm.org/doi/10.1007/s10915-023-02166-w

Index Terms

Strong Stability of Explicit Runge--Kutta Time Discretizations
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Computations on matrices
      2. Numerical differentiation

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 57, Issue 3

DOI:10.1137/sjnaam.57.3

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© 2019, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2019

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Cited By

Xu YShu CZhang Q(2024)Stability Analysis and Error Estimate of the Explicit Single-Step Time-Marching Discontinuous Galerkin Methods with Stage-Dependent Numerical Flux Parameters for a Linear Hyperbolic Equation in One DimensionJournal of Scientific Computing10.1007/s10915-024-02621-2100:3Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1007/s10915-024-02621-2
Sun ZXing Y(2023)On Generalized Gauss–Radau Projections and Optimal Error Estimates of Upwind-Biased DG Methods for the Linear Advection Equation on Special Simplex MeshesJournal of Scientific Computing10.1007/s10915-023-02166-w95:2Online publication date: 18-Mar-2023
https://dl.acm.org/doi/10.1007/s10915-023-02166-w

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