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
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
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
SIAM Journal on Numerical Analysis
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Step Sizes for Strong Stability Preservation with Downwind-Biased Operators
SIAM Journal on Numerical Analysis
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Computers & Mathematics with Applications
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In the field of strong-stability-preserving time discretizations, a number of researchers have considered using both upwind and downwind approximations for the same derivative, in order to guarantee that some strong stability condition will be preserved. The cost of computing both the upwind and downwind operator has always been assumed to be double that of computing only one of the two. However, in this paper we show that for the weighted essentially non-oscillatory method it is often possible to compute both these operators at a cost that is far below twice the cost of computing only one. This gives rise to the need for optimal strong-stability-preserving time-stepping schemes which take into account the different possible cost increments. We construct explicit linear multistep schemes up to order six and explicit Runge---Kutta schemes up to order four which are optimal over a range of incremental costs