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| Study on adaptive step size of precise intrgration method for nonlinear dynamic equations |
| Received:June 30, 2020 Revised:September 14, 2020 |
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| DOI：10.7511/jslx20200630001 |
| KeyWord:nonlinear dynamic equations adaptive step precise integration estimation formula |
| Author | Institution |
| 王海波 |
中南大学 土木工程学院, 长沙 |
| 纪海潮 |
中南大学 土木工程学院, 长沙 |
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| Abstract: |
| In this paper,the adaptive selection of time steps is realized based on Adams explicit and implicit estimation formulas:For the state equation used for a nonlinear dynamic system,given v(tk) at the current time instant,two forms of the prediction formula (explicit and implicit) were used to respectively estimate the truncation errors,and the obtain ξ(tk+1) was taken as the error of this time step,and the value of the time step was adjusted according to the value of the result.This idea is applied to the precise integration algorithm of the predictive type (the solution process needs to use the prediction formula),making the time step of the precise integration algorithm depend on the given error limit of each step,improving the calculation accuracy,and making the algorithm have good stability,and have good effect on the stiffness hardening and softening problems.Numerical examples demonstrate the validity and applicability of the proposed ideas. |
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