Strong stability preserving two-derivative multistep Runge–Kutta methods

We introduce the explicit strong stability preserving (SSP) two-derivative multistep Runge–Kutta (TDMSRK) methods. The order accuracy conditions and SSP theory for the TDMSRK methods are developed. By comparing the SSP coefficients of TDMSRK methods, Runge–Kutta schemes, two-derivative Runge–Kutta schemes, and general linear methods, it is indicated that the TDMSRK schemes have the largest effective SSP coefficient at the same order of accuracy. Some classical tests demonstrate the numerical stability of the TDMSRK methods on the Euler equation. Furthermore, the TDMSRK methods can achieve the expected order of accuracy and exhibit high computational efficiency in solving the Euler equation.