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

DOI10.1137/19M1290346zbMath1457.65032arXiv1909.13215MaRDI QIDQ3386989

David I. Ketcheson, Hendrik Ranocha

Publication date: 12 January 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.13215

zbMATH Keywords

dissipationsemiboundednessRunge-Kutta methodsstrong stabilityconservationenergy stability

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (8)

A new kinetic-energy-preserving method based on the convective rotational form ⋮ Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes ⋮ Diagonally implicit Runge-Kutta schemes: discrete energy-balance laws and compactness properties ⋮ A new class of \(A\) stable summation by parts time integration schemes with strong initial conditions ⋮ Enforcing strong stability of explicit Runge-Kutta methods with superviscosity ⋮ Issues with positivity-preserving Patankar-type schemes ⋮ On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems ⋮ Stability of structure-aware Taylor methods for tents

Uses Software

• RODAS
• Julia
• GitHub
• DifferentialEquations.jl
• RRK_rr
• InductionEq
• NeuralPDE.jl

Cites Work

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