Stability and Accuracy of Wilson－θ Method with Modified Acceleration
There remain two kinds of the Wilson-θ methods, the Wilson-θ and methods named by author. In the Wilson-θ method, the accelerations are not modified by the dynamic equilibrium equations at the time ; in the Wilson-θ method, the accelerations are modified. The amplification matrixes of the Wilson-θ and methods for single-degree-of-freedom system are derived. The stabilities of the Wilson-θ and methods are examined by the spectral radii of the amplification matrixes. The stability of the Wilson-θ method is unconditional for . The calculation results indicate: the stability of the Wilson-θ method is not unconditional, its improvement of accuracy is slight; both the stability range and accuracy are less than the ones of the linear acceleration method, so the Wilson-θ method wouldn't be adopted.
Jingtao Han, Zhengyi Jiang and Sihai Jiao
D. P. Fang and Q. F. Wang, "Stability and Accuracy of Wilson－θ Method with Modified Acceleration", Advanced Materials Research, Vols. 156-157, pp. 132-136, 2011