Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

Effective order strong stability preserving RungeKutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of ef...

Optimal Explicit Strong-Stability-Preserving General Linear Methods

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A glo...

Optimal Explicit Strong - Stability - Preserving

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge–Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A glo...

A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods

Strong Stability-Preserving High-Order Time Discretization Methods

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial di erential equations. Termed TVD (total variation diminishing) time discretizations before, this class of high-order time discretization methods preserves the strong-stability properties of rst-order Euler time step...