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
A positive finite-difference advection scheme
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
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
Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
Representations of Runge-Kutta Methods and Strong Stability Preserving Methods
SIAM Journal on Numerical Analysis
Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems
SIAM Journal on Numerical Analysis
Linear Instability of the Fifth-Order WENO Method
SIAM Journal on Numerical Analysis
Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations
SIAM Journal on Scientific Computing
Optimal implicit strong stability preserving Runge--Kutta methods
Applied Numerical Mathematics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
On the positivity step size threshold of Runge--Kutta methods
Applied Numerical Mathematics
An improvement on the positivity results for 2-stage explicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
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In this paper we consider Strong Stability Preserving (SSP) properties for explicit Runge---Kutta (RK) methods applied to a class of nonlinear ordinary differential equations. We define new modified threshold factors that allow us to prove properties, provided that they hold for explicit Euler steps. For many methods, the stepsize restrictions obtained are sharper than the ones obtained in terms of the Kraaijevanger's coefficient in the SSP theory. In particular, for the classical 4-stage fourth order method we get nontrivial stepsize restrictions. Furthermore, the order barrier $$p\le 4$$ p ≤ 4 for explicit SSP RK methods is not obtained. An open question is the existence of explicit RK schemes with order $$p\ge 5$$ p 驴 5 and nontrivial modified threshold factor. The numerical experiments done illustrate the results obtained.