Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Two Barriers on Strong-Stability-Preserving Time Discretization Methods
Journal of Scientific Computing
Journal of Scientific Computing
Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
On Strong Stability Preserving Time Discretization Methods
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational Physics
High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set
Journal of Computational Physics
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
Optimal implicit strong stability preserving Runge--Kutta methods
Applied Numerical Mathematics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Strong stability preserving hybrid methods
Applied Numerical Mathematics
Characterizing Strong Stability Preserving Additive Runge-Kutta Methods
Journal of Scientific Computing
Explicit Time Stepping Methods with High Stage Order and Monotonicity Properties
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Journal of Computational Physics
A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver
Journal of Scientific Computing
Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods
Applied Numerical Mathematics
Optimal Explicit Strong-Stability-Preserving General Linear Methods
SIAM Journal on Scientific Computing
Strong-Stability-Preserving 7-Stage Hermite---Birkhoff Time-Discretization Methods
Journal of Scientific Computing
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Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties---in any norm or seminorm--of the spatial discretization coupled with first order Euler time stepping. This paper describes the development of SSP methods and the recently developed theory which connects the timestep restriction on SSP methods with the theory of monotonicity and contractivity. Optimal explicit SSP Runge---Kutta methods for nonlinear problems and for linear problems as well as implicit Runge---Kutta methods and multi step methods will be collected