A simple and efficient fourth-order approximation solution for nonlinear dynamic system

Zhang, Suying; Deng, Zichen

doi:10.1016/j.mechrescom.2003.10.004

Cited by 8 publications

(2 citation statements)

References 12 publications

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“…Further research will intend to extend the proposed method to the non homogeneous case and non-linear case. It might be advantageous to use the Lie transform [13] to convert the non-linear equation into the autonomous equation and modified Magnus integrator method can treat it as our proposed method.…”

Section: Discussionmentioning

confidence: 99%

Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

2006

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Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method was proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the secondorder dynamic system was reformulated as the first-order system and the frame of reference was transfered by introducing new variables so that highly oscillatory behaviour inherits 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 also were presented. Finally, numerical examples 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

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Section: Discussionmentioning

confidence: 99%

Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

2006

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“…Then we can obtain a fourth-order method using (8) Firstly, the computations require us to find Ω [3] (h),…”

Section: Numerical Integrators For Nonlinear Equations 21 Numerical mentioning

confidence: 99%

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

Deng

2008

Appl. Math. Mech.-Engl. Ed.

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Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.

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A Lie-groupDSO(n)method for nonlinear dynamical systems

Liu

2013

Applied Mathematics Letters

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A simple and efficient fourth-order approximation solution for nonlinear dynamic system

Cited by 8 publications

References 12 publications

Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

A Lie-groupDSO(n)method for nonlinear dynamical systems

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