Strong-stability-preserving Hermite–Birkhoff Timediscretization Methods Combining k-step Methods and Explicit s-stage RK4 Methods

2012
Truong Nguyen-Ba, Huong Nguyen-Thu, Thierry Giordano, Rémi Vaillancourt

New optimal strong-stability-preserving Hermite– Birkhoff (SSP HB) methods, HB(k, s, p), of order p = 4, 5, . . . , 12, are constructed by combining k-step methods of order p = 1, 2, ...,9 and s-stage explicit Runge–Kutta (RK) methods of order 4, where s = 4, 5, . . . , 10. These methods are well suited for solving discretized hyperbolic PDEs by the method of lines. The Shu– Osher form of RK methods is extended to our new methods. The HB(k, s, p) having the largest effective SSP coefficient have been numerically found among the HB methods of order p on hand. These SSP high-order methods are compared with other SSP methods and their main features are summarized.

Keywords
Strong stability preserving; 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 Hermite–Birkhoff Timediscretization Methods Combining k-step Methods and Explicit s-stage RK4 Methods. Boundary Field Problems and Computer Simulation. Vol.51, 2012, pp.57-69. ISSN 2255-9124. e-ISSN 2255-9132.

Publication language
English (en)