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| Precise integration method for sensitivity analysis of linear ODEs |
| Received:July 16, 2007 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20094001 |
| KeyWord:Precise time integration matrix exponential derivatives of matrix exponential sensitivity analysis |
| Author | Institution |
| 刘诗源 |
大连理工大学 运载工程与力学学部 工业装备结构分析国家重点实验室,大连 |
| 陈飙松 |
大连理工大学 运载工程与力学学部 工业装备结构分析国家重点实验室,大连 |
| 丁海宽 |
中国石油吉林石化分公司 乙二醇厂,吉林 |
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| Abstract: |
| In this paper, the derivatives of matrix exponential is employed to solve the sensitivity analysis of linear ordinary differential equations(ODEs) with respect to a given design variable. For the initial value problems, the derivatives of state vector with respect to design variables can be obtained by using the derivatives of matrix exponential. For the two-point boundary value problem, the matrix exponential and its derivatives are employed to link the boundary derivative conditions between the two points. With full conditions at initial point, the liner two-point boundary value problems can be transformed into initial value problem and then solved by time marching scheme. The computation of matrix exponential and its derivatives are performed based on 2N algorithm. And then sensitivity analysis can be carried out. Sensitivity analysis method with high numerical precision is developed. Numerical examples demonstrate the extremely high numerical precision of the method. |
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