Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
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
Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
SIAM Journal on Numerical Analysis
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations
SIAM Journal on Scientific Computing
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Strong stability preserving hybrid methods
Applied Numerical Mathematics
A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11
Journal of Computational and Applied Mathematics
Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations
Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations
Strong-Stability-Preserving 7-Stage Hermite---Birkhoff Time-Discretization Methods
Journal of Scientific Computing
Hi-index | 7.29 |
Ruuth and Spiteri have shown, in 2002, that fifth-order strong-stability-preserving (SSP) explicit Runge-Kutta (RK) methods with nonnegative coefficients do not exist. One of the purposes of the present paper is to show that the Ruuth-Spiteri barrier can be broken by adding backsteps to RK methods. New optimal, 8-stage, explicit, SSP, Hermite-Birkhoff (HB) time discretizations of order p, p=5,6,...,12, with nonnegative coefficients are constructed by combining linear k-step methods of order (p-4) with an 8-stage explicit RK method of order 5 (RK(8, 5)). These new SSP HB methods preserve the monotonicity property of the solution and prevent error growth; therefore, they are suitable for solving hyperbolic partial differential equations (PDEs) by the method of lines. Moreover, these new HB methods have larger effective SSP coefficients and larger maximum effective CFL numbers than Huang's hybrid methods and RK methods of the same order when applied to the inviscid Burgers equation. Generally, HB methods combined with RK(8, 5) have maximum stepsize 24% larger than HB combined with RK(8, 4).