This paper derives a new family of implicit–explicit time-marching methods for PDEs with the
second-order derivative in time. The present implicit method is based on the two-derivative
Runge–Kutta–Nyström methods, which use a third-order time derivative of the solution.
Although the current approach is implicit, it does not need to invert the coefficient matrix of
the discretized system of equations. The stability properties are assessed using Fourier
analysis for the model test problems by considering space–time discretizations together. The …