Abstract:Eight step-by-step time-integration methods are introduced,and their stability and computational accuracy are analyzed and compared systemically. The definitions of theoretical accuracy and computational accuracy of step-by-step time-integration methods are introduced. The theoretical accuracy of the method is the accuracy when step time approaches to be zero. While in practical computation,the step time is always chosen as large as possible under the precondition of stability demand;and the accuracy the method shows at this time is defined as computational accuracy. The analysis shows that the computational accuracy of a method deviates from its theoretical accuracy and is consistent with its amplitude decay rate and period elongation. Until now,few attention has been paid to the study of computational accuracy. The computational accuracy of the methods is analyzed theoretically;and the amplitude decay and period elongation of the methods are formulated under undamped case. Numerical examples including linear-elastic and elastoplastic vibrations of structure with single degree of freedom are computed;and the behaviors of the methods in elastoplastic condition are analyzed preliminarily. Combining calculation results with theoretical analysis,the eight methods¢ behaviors in practical computation are clearly demonstrated. Thus,references are provided to select an appropriate step-by-step time-integration method in practical computation.