Embedded pairs for optimal explicit strong stability preserving Runge-Kutta methods

DOI10.1016/j.cam.2022.114325zbMath1495.65115OpenAlexW4224102766MaRDI QIDQ2141605

John N. Shadid, Sidafa Conde, Imre Fekete

Publication date: 25 May 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2022.114325

zbMATH Keywords

Runge-Kutta methodshyperbolic problemsembedded pairsvariable step-sizestep-size controlstrong stability preserving methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (5)

Derivation of third order Runge-Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation ⋮ Adaptive step size controllers based on Runge-Kutta and linear-neighbor methods for solving the non-stationary heat conduction equation ⋮ Embedded paired explicit Runge-Kutta schemes ⋮ Unconditionally positive, explicit, fourth order method for the diffusion- and Nagumo-type diffusion-reaction equations ⋮ Optimized Runge-Kutta methods with automatic step size control for compressible computational fluid dynamics

Uses Software

• Matlab
• SUNDIALS
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• NodePy
• MATLAB ODE suite
• GitHub
• ImplicitLNLMethods
• imexLNL

Cites Work

• SUNDIALS
• A 3(2) pair of Runge-Kutta formulas
• Stability radius of polynomials occurring in the numerical solution of initial value problems
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• A family of embedded Runge-Kutta formulae
• Contractivity of Runge-Kutta methods
• Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
• Implicit and implicit-explicit strong stability preserving Runge-Kutta methods with high linear order
• On strong stability preserving time discretization methods
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Automatic control and adaptive time-stepping
• Efficient implementation of weighted ENO schemes
• Time-step selection algorithms: adaptivity, control, and signal processing
• Strong Stability Preserving Time Discretizations: A Review
• The MATLAB ODE Suite
• Solving Ordinary Differential Equations I
• Total-Variation-Diminishing Time Discretizations
• Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
• Total variation diminishing Runge-Kutta schemes
• Finite Volume Methods for Hyperbolic Problems
• A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
• Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
• Digital filters in adaptive time-stepping
• Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order
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