Highly accurate ρ method for structural dynamic analysis

The paper proposes a ρ method of unconditionally stable direct integration with the fourth-order and fifth-order accuracy. The ρ method shows a good algorithmic damping and period extension property, and we don't find any overshooting phenomenon. It needs less calculation and storage space than other methods of high accuracy. It doesn't require that the damping matrix satisfy the condition of orthogonality of modes in order to prove its unconditional stability.