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
High-order explicit Runge-Kutta pairs with low stage order
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Two Barriers on Strong-Stability-Preserving Time Discretization Methods
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Two Barriers on Strong-Stability-Preserving Time Discretization Methods
Journal of Scientific Computing
On Strong Stability Preserving Time Discretization Methods
Journal of Scientific Computing
High-order RKDG Methods for Computational Electromagnetics
Journal of Scientific Computing
On High Order Strong Stability Preserving Runge---Kutta and Multi Step Time Discretizations
Journal of Scientific Computing
High-order RKDG methods for computational electromagnetics
Journal of Scientific Computing
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Strong stability preserving hybrid methods
Applied Numerical Mathematics
Journal of Computational Physics
Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods
Applied Numerical Mathematics
Journal of Computational Physics
Hi-index | 0.01 |
Strong stability preserving (SSP) high order Runge–Kutta time discretizations were developed for use with semi-discrete method of lines approximations of hyperbolic partial differential equations, and have proven useful in many other applications. These high order time discretization methods preserve the strong stability properties of first order explicit Euler time stepping. In this paper we analyze the SSP properties of Runge Kutta methods for the ordinary differential equation ut=Lu where L is a linear operator. We present optimal SSP Runge–Kutta methods as well as a bound on the optimal timestep restriction. Furthermore, we extend the class of SSP Runge–Kutta methods for linear operators to include the case of time dependent boundary conditions, or a time dependent forcing term.