  This paper proposes several explicit and implicit multistep frequency
response optimized integrators considering first or second order derivative. A
prediction-based method aiming at accelerating a novel power system transient
simulation scheme without impacting its accuracy is further put forward
utilizing the proposed numerical integrators and some others available in the
literature. Case studies verify the effectiveness of the proposed prediction
method. Although they are utilized to accelerate the simulation scheme in this
paper, the proposed numerical integrators are in fact general-purpose and can
be applied to other areas.
