Strong-stability-preserving Hermite - Birkhoff time discretization methods combining k-step methods and explicit s-stage Runge-Kutta methods of order 5

Abstract

New optimal strong-stability-preserving (SSP) Hermite-Birkhoff (HB) methods, HB(k,s,p) of order p = 5,6,...,12 with nonnegative coefficients, are constructed by combining k -step methods of order (p - 4) and s -stage explicit Runge-Kutta methods of order 5 (RK5), where s = 4,5,...,10. These new methods preserve the monotonicity property of the solution, so they are suitable for solving ordinary differential equations (ODEs) coming from spatial discretization of hyperbolic partial differential equations (PDEs). The canonical Shu -