Two Barriers on Strong-Stability-Preserving Time Discretization Methods
Journal of Scientific Computing
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
Construction of Shapes Arising from the Minkowski Problem Using a Level Set Approach
Journal of Scientific Computing
On Strong Stability Preserving Time Discretization Methods
Journal of Scientific Computing
RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
High-order RKDG Methods for Computational Electromagnetics
Journal of Scientific Computing
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
On High Order Strong Stability Preserving Runge---Kutta and Multi Step Time Discretizations
Journal of Scientific Computing
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
High-order RKDG methods for computational electromagnetics
Journal of Scientific Computing
On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws
Journal of Scientific Computing
Optimal Strong-Stability-Preserving Time-Stepping Schemes with Fast Downwind Spatial Discretizations
Journal of Scientific Computing
Journal of Computational Physics
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
Stepsize restrictions for total-variation-boundedness in general Runge-Kutta procedures
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
3D transient fixed point mesh adaptation for time-dependent problems: Application to CFD simulations
Journal of Computational Physics
Journal of Computational Physics
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD
Journal of Computational Physics
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
An improved reconstruction method for compressible flows with low Mach number features
Journal of Computational Physics
On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes
Journal of Computational Physics
A Local Semi-Implicit Level-Set Method for Interface Motion
Journal of Scientific Computing
The Flexible, Extensible and Efficient Toolbox of Level Set Methods
Journal of Scientific Computing
A Numerical Study of Diagonally Split Runge---Kutta Methods for PDEs with Discontinuities
Journal of Scientific Computing
Strong stability of singly-diagonally-implicit Runge--Kutta methods
Applied Numerical Mathematics
Finite volume and WENO scheme in one-dimensional vascular system modelling
Computers & Mathematics with Applications
Optimal implicit strong stability preserving Runge--Kutta methods
Applied Numerical Mathematics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Spectral difference method for compressible flow on unstructured grids with mixed elements
Journal of Computational Physics
Strong stability preserving hybrid methods
Applied Numerical Mathematics
Characterizing Strong Stability Preserving Additive Runge-Kutta Methods
Journal of Scientific Computing
Stepsize restrictions for total-variation-boundedness in general Runge--Kutta procedures
Applied Numerical Mathematics
High-order sonic boom modeling based on adaptive methods
Journal of Computational Physics
Journal of Computational Physics
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods
Applied Numerical Mathematics
Finite volume schemes for dispersive wave propagation and runup
Journal of Computational Physics
Optimal Explicit Strong-Stability-Preserving General Linear Methods
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Computers & Mathematics with Applications
Strong-Stability-Preserving 7-Stage Hermite---Birkhoff Time-Discretization Methods
Journal of Scientific Computing
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model
International Journal of High Performance Computing Applications
Journal of Computational Physics
Journal of Computational Physics
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
Strong Stability Preserving Two-step Runge-Kutta Methods
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Journal of Computational Physics
Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Computers & Mathematics with Applications
A ghost fluid method for compressible reacting flows with phase change
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Strong Stability for Runge---Kutta Schemes on a Class of Nonlinear Problems
Journal of Scientific Computing
Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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Strong-stability-preserving (SSP) time discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws where discontinuous behavior is present. Optimal SSP schemes have been previously found for methods of order 1, 2, and 3, where the number of stages s equals the order p. An optimal low-storage SSP scheme with s=p=3 is also known. In this paper, we present a new class of optimal high-order SSP and low-storage SSP Runge--Kutta schemes with sp. We find that these schemes are ultimately more efficient than the known schemes with s=p because the increase in the allowable time step more than offsets the added computational expense per step. We demonstrate these efficiencies on a set of scalar conservation laws.