Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
A new theoretical approach to Runge-Kutta methods
SIAM Journal on Numerical Analysis
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 general class of two-step Runge-Kutta methods for ordinary differential equations
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
The Runge-Kutta Theory in a Nutshell
SIAM Journal on Numerical Analysis
Order conditions for two-step Runge-Kutta methods
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Order Conditions for General Two-Step Runge--Kutta Methods
SIAM Journal on Numerical Analysis
A PDE-based fast local level set method
Journal of Computational Physics
Journal of Computational Physics
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
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
On Strong Stability Preserving Time Discretization Methods
Journal of Scientific Computing
Journal of Computational Physics
Representations of Runge-Kutta Methods and Strong Stability Preserving Methods
SIAM Journal on Numerical Analysis
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
A spectral finite volume transport scheme on the cubed-sphere
Applied Numerical Mathematics
Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems
SIAM Journal on Numerical Analysis
A Numerical Study of Diagonally Split Runge---Kutta Methods for PDEs with Discontinuities
Journal of Scientific Computing
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
Strong stability preserving hybrid methods
Applied Numerical Mathematics
Journal of Computational Physics
Improved starting methods for two-step Runge--Kutta methods of stage-order p-3
Applied Numerical Mathematics
Runge-Kutta methods with minimum storage implementations
Journal of Computational Physics
Starting methods for two-step Runge-Kutta methods of stage-order 3 and order 6
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
Journal of Computational Physics
Optimal Explicit Strong-Stability-Preserving General Linear Methods
SIAM Journal on Scientific Computing
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We investigate the strong stability preserving (SSP) property of two-step Runge-Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge-Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present explicit TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order weighted essentially non-oscillatory discretizations.