Numerical Integration Algorithm of the Symplectic-Conservative and Energy-Preserving Method

SUN Yan; GAO Qiang; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2014.08.001

Volume 35 Issue 8

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SUN Yan, GAO Qiang, ZHONG Wan-xie. Numerical Integration Algorithm of the Symplectic-Conservative and Energy-Preserving Method[J]. Applied Mathematics and Mechanics, 2014, 35(8): 831-837. doi: 10.3879/j.issn.1000-0887.2014.08.001

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Numerical Integration Algorithm of the Symplectic-Conservative and Energy-Preserving Method

doi: 10.3879/j.issn.1000-0887.2014.08.001

¹Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;²State Key Laboratory of Structural Analysis of Industrial Equipment(Dilian University of Technology); Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China(51278298); The National Hightech R&D Program of China (863 Program)(2012AA022606)

Received Date: 2014-05-29
Rev Recd Date: 2014-06-30
Publish Date: 2014-08-15

Abstract

Abstract

A symplectic-conservative algorithm was proposed for the nonlinear dynamic Hamilton systems with the application of the mixed energy variational principle. Based on this, an iterative algorithm for the nonlinear problem was designed in which a parametric variable was introduced into the Hamilton system, and the goal of energy preservation was realized at the integration grid nodes through parametric adjustments. The numerical examples of the undamped Duffing spring systems show that, compared with the only symplectic-conservative algorithm, the proposed symplectic-conservative and energy-preserving algorithm bears far higher accuracy in the simulation of the nonlinear dynamic Hamilton systems.
- symplectic-conservative,
- energy-preserving,
- Hamilton system,
- interval mixed energy,
- parametric variable

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References(6)

References

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