Some notes on summation by parts time integration methods

DOI10.1016/j.rinam.2019.100004zbMath1453.65161arXiv1901.08377OpenAlexW2911611941WikidataQ128182889 ScholiaQ128182889MaRDI QIDQ2211049

Hendrik Ranocha

Publication date: 10 November 2020

Published in: Results in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.08377

zbMATH Keywords

time integrationRunge-Kutta methodsummation by partsstrong stability preserving

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (10)

Properties of Runge-Kutta-summation-by-parts methods ⋮ Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators ⋮ Resolving entropy growth from iterative methods ⋮ Theoretical and practical aspects of space-time DG-SEM implementations ⋮ Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier-Stokes equations ⋮ General relaxation methods for initial-value problems with application to multistep schemes ⋮ A new class of \(A\) stable summation by parts time integration schemes with strong initial conditions ⋮ Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems ⋮ Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods ⋮ On an eigenvalue property of summation-by-parts operators

Uses Software

• Mathematica
• RODAS
• NodePy

Cites Work

• Unnamed Item
• Summation-by-parts in time
• Review of summation-by-parts schemes for initial-boundary-value problems
• The SBP-SAT technique for initial value problems
• A generalized framework for nodal first derivative summation-by-parts operators
• On pseudo-spectral time discretizations in summation-by-parts form
• Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
• High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators
• Solving Ordinary Differential Equations II

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