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| Increment-dimensional precise integration method based on cubic spline interpolation for nonlinear dynamic equation |
| Received:July 10, 2013 Revised:October 18, 2013 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201406008 |
| KeyWord:nonlinear dynamic equation precise integration increment-dimension cubic spline interpolation predict-correct |
| Author | Institution |
| 凌明祥 |
中国工程物理研究院 总体工程研究所, 绵阳 |
| 韩宇航 |
中国工程物理研究院 总体工程研究所, 绵阳 |
| 朱长春 |
中国工程物理研究院 总体工程研究所, 绵阳 |
| 王天忠 |
中国工程物理研究院 总体工程研究所, 绵阳 |
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| Abstract: |
| An improved precise integration method for nonlinear dynamic equations was proposed in this paper.The inhomogeneous terms were fitted by employing piecewise cubic spline interpolation at ever time-step to increase fitting precision and to avoid calculating differential coefficient,curve oscillation of high-order polynomial fitting was also avoided.The original nonlinear dynamic equations were converted into homogenous equations with four increased dimensions by importing 4×2 variables,the relevant calculating format was built without inversing the state-space system matrix.Based on the mathematic feature of homogenized matrix,a partitioning and step by step precise integration calculating method was presented by theoretical deducing and blocked calculation,no need for computing matrix exponential at every time step,and the efficiency was improved.Predict-correct method based on Taylor format was used for inhomogeneous terms with state variables.The numerical examples show that high precision and fast speed were achieved. |