Strong-Stability-Preserving, K-Step, 6- to 10-Stage, Hermite–Birkhoff Time-Discretizations of Order 7

2011
Truong Nguyen-Ba, Huong Nguyen-Thu, Thierry Giordano, Rémi Vaillancourt

Optimal k-step, 6- to 10-stage, explicit, strong-stability-preserving Hermite–Birkhoff (SSP HB) methods of order 7 with nonnegative coefficients are constructed by combining linear k-step methods of order 4 with 6- to 10-stage Runge–Kutta (RK) methods of order 4. It is seen that the 6-step 6-stage HB method has the largest effective SSP coefficient among the 7th-order HB methods on hand. All new HB methods have larger effective SSP coefficients and larger maximum effective CFL numbers than Huang’s hybrid method of order 7, on Burgers’ equations, independently of the number k of steps.

Keywords
Strong-stability-preserving method; Hermite–Birkhoff method; SSP coefficient; time discretization; method of lines; comparison with other SSP methods.

Nguyen-Ba, T., Nguyen-Thu, H., Giordano, T., Vaillancourt, R. Strong-Stability-Preserving, K-Step, 6- to 10-Stage, Hermite–Birkhoff Time-Discretizations of Order 7. Boundary Field Problems and Computer Simulation. Vol.50, 2011, pp.76-85. ISSN 1407-7493.

Publication language
English (en)