General relaxation methods for initial-value problems with application to multistep schemes
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Publication:2217872
DOI10.1007/s00211-020-01158-4zbMath1456.65051arXiv2003.03012OpenAlexW3096719680MaRDI QIDQ2217872
Hendrik Ranocha, David I. Ketcheson, Lajos Lóczi
Publication date: 11 January 2021
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.03012
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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
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Cites Work
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- Numerical methods for non conservative perturbations of conservative problems
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- Review of summation-by-parts schemes for initial-boundary-value problems
- Entropy-dissipating semi-discrete Runge-Kutta schemes for nonlinear diffusion equations
- Stability of the fourth order Runge-Kutta method for time-dependent partial differential equations
- Invariants preserving schemes based on explicit Runge-Kutta methods
- Relaxation Runge-Kutta methods for Hamiltonian problems
- Projection methods preserving Lyapunov functions
- A method for the integration in time of certain partial differential equations
- An explicit finite-difference scheme with exact conservation properties
- Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation
- A high-order conservative Patankar-type discretisation for stiff systems of production--destruction equations
- Regular and singular \(\beta\)-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
- On the zero-stability of multistep methods on smooth nonuniform grids
- An entropy stable \(h/p\) non-conforming discontinuous Galerkin method with the summation-by-parts property
- \(L_2\) stability of explicit Runge-Kutta schemes
- On discretely entropy conservative and entropy stable discontinuous Galerkin methods
- High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows
- Comparison of some entropy conservative numerical fluxes for the Euler equations
- Entropy production by explicit Runge-Kutta schemes
- Artificial viscosity for correction procedure via reconstruction using summation-by-parts operators
- Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators
- Conservation laws and the numerical solution of ODEs. II
- Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier-Stokes equations
- Some notes on summation by parts time integration methods
- Entropy production by implicit Runge-Kutta schemes
- Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws
- High-order linear multistep methods with general monotonicity and boundedness properties
- Geometric integration methods that preserve Lyapunov functions
- Monotonicity for Runge-Kutta methods: inner product norms
- Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size
- Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints
- On the Preservation of Invariants by Explicit Runge--Kutta Methods
- High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators
- Non-linear stability of a general class of differential equation methods
- Stability Criteria for Implicit Runge–Kutta Methods
- Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
- Energy stable boundary conditions for the nonlinear incompressible Navier–Stokes equations
- A Polynomial Formulation of Adaptive Strong Stability Preserving Multistep Methods
- High-order accurate, fully discrete entropy stable schemes for scalar conservation laws
- Grid-Independent Construction of Multistep Methods
- Maintaining Solution Invariants in the Numerical Solution of ODE<scp>s</scp>
- Fully Discrete, Entropy Conservative Schemes of ArbitraryOrder
- On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators
- Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods
- Solving Ordinary Differential Equations II
- Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms
- Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
- Strong Stability of Explicit Runge--Kutta Time Discretizations
- Geometric Numerical Integration
- Integration of Stiff Equations
- Numerical Methods for Ordinary Differential Equations
- Hyperbolic Conservation Laws in Continuum Physics
