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Symplectic two-step algorithms of FE dynamic equations. (Chinese. English summary) Zbl 1189.70059

Summary: Two symplectic two-step solution algorithms of finite element dynamics equilibrium equations are presented, one of which has fourth order of accuracy, the phase is forward, and the accuracy of the other is of second order, the phase is backward. The calculation work of the fourth order two-step methods is not bigger than that of the Newmark symplectic method whose accuracy is of second order, so there is an advantage of the fourth order two-step symplectic algorithm in the application to the practical calculation. The phase errors of the fourth order algorithm are compared in detail with that of the Newmark symplectic method. Numerical results are given to illustrate the accuracy of the newly constructed two-step algorithm by comparing the obtained dynamic responses and energy with that of symplectic Newmark and analytical methods.

MSC:

70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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