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
Citation:
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
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
Citation:
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
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 Hightech R&D Program of China (863 Program)(2012AA022606)
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.
Zhong G, Marsden J E. Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators[J]. Physics Letter A,1988,113(3): 134-139.
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