Efficient Numerical Integrators for Highly Oscillatory Dynamic Systems Based on Modified Magnus Integrator Method

LI Wen-cheng; DENG Zi-chen; HUANG Yong-an

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(10): 1211-1218

LI Wen-cheng, DENG Zi-chen, HUANG Yong-an. Efficient Numerical Integrators for Highly Oscillatory Dynamic Systems Based on Modified Magnus Integrator Method[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1211-1218.

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Efficient Numerical Integrators for Highly Oscillatory Dynamic Systems Based on Modified Magnus Integrator Method

1.
School of Science, Northwestern Polytechnical University, Xi'an 710072, P. R. China;
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, P. R. China;
State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China

Received Date: 2005-08-16
Rev Recd Date: 2006-04-06
Publish Date: 2006-10-15

Abstract

Abstract

Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method is proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the second-order dynamic system was reformulated as a system of the first-order and transfered the frame of reference by introducing new variables so that highly oscillatory behaviour is inherited from the entries in the meantime. Then the modified Magnus integrator method based on local linearization was appropriately-designed for solving the above new form and some improved ones are also presented. Finally, numerical examples are presented and analyzed to show that the proposed methods appear to be quite adequate for integration for highly oscillatory dynamic systems including Hamiltonian systems problem with long time and effectiveness.
- dynamic systems,
- highly oscillatory,
- Magnus integrator method,
- Hamiltonian systems

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References(13)

References

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