The stability and accuracy of two families of time integration algorithms are investigated in this study. The paper has three intended goals. The first one is to find the precise properties of the implicit higher-order accuracy methods. The capabilities of the family members are found both by analytical and numerical procedures. The second goal is to find the well-defined characteristics of the predictor–corrector methods. For application purposes, the best order of each family is introduced by this investigation. Numerical results show that the stability properties of the implicit high-order accuracy and predictor–corrector methods are approximately the same. As a third goal, a modified dynamic relaxation method is also developed for non-linear dynamic analyses. This is a robust scheme that uses less memory and requires less computational effort, in comparison with the previous version of dynamic relaxation method.

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