Strong-Stability-Preserving 7-Stage Hermite-Birkhoff Time-Discretization Methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of 4-stage explicit SSP Hermite-Birkhoff methods of orders 4 to 8 with nonnegative coefficients are constructed as k-step analogues of fourth-order Runge-Kutta methods with three off-step points. Generally, they have high-stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. The new methods generally have larger effective SSP coefficients and larger maximum effective CFL numbers than Huang’s hybrid methods of the same order on Burgers’ equations, independently of the number of steps. This is more so when the number of steps is small.