SUMMARYThe integration step size is the main algorithmic parameter in time integration analysis. Nowadays, for time integration with the complete records of digitized excitations, the integration steps cannot be set larger than the excitation steps. Considering the practical importance of this restriction, and with the aim of structural dynamic analysis with less computational cost, this paper intends to extend conventional time integration analyses to analyses, if needed, carried out with steps larger than the excitations steps. In view of few simplifying assumptions, and presenting a new theorem on responses convergence, a technique is developed and a computational procedure is set. Being based on convergence-oriented redefinition of digitized excitations, the implementation of the new procedure is simple and, though, sacrificing some accuracy, can considerably reduce the total computational cost.

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SUMMARYThe results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error-controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering.

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