The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
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
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
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
Monotonicity for Runge--Kutta Methods: Inner Product Norms
Journal of Scientific Computing
Representations of Runge-Kutta Methods and Strong Stability Preserving Methods
SIAM Journal on Numerical Analysis
On High Order Strong Stability Preserving Runge---Kutta and Multi Step Time Discretizations
Journal of Scientific Computing
Contractivity/monotonicity for additive Runge-Kutta methods: inner product norms
Applied Numerical Mathematics
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
Contractivity/monotonicity for additive Runge--Kutta methods: Inner product norms
Applied Numerical Mathematics
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
Nonlinear OIFS for a hybrid galerkin atmospheric model
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
High-Order finite element methods for parallel atmospheric modeling
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
On the accuracy of high-order finite elements in curvilinear coordinates
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Strong Stability Preserving Two-step Runge-Kutta Methods
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
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Over the last few years, great effort has been made to develop high order strong stability preserving (SSP) Runge–Kutta methods. These methods have a nonlinear stability property that makes them suitable for the time integration of ODEs that arise from a method of lines approximation of hyperbolic conservation laws. Basically, this stability property is a monotonicity property for the internal stages and the numerical solution. Recently Ferracina and Spijker have established a link between stepsize restrictions for monotonicity and the already known stepsize restrictions for contractivity. Hence the extensive research on contractivity can be transferred to the SSP context. In this paper we consider monotonicity issues for arbitrary norms and linear and nonlinear problems. We collect and review some known results and relate them with the ones obtained in the SSP context.