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

Suying Zhang; Zichen Deng

doi:10.1016/j.mechrescom.2003.10.004

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

Suying Zhang, Zichen Deng

School of Aeronautics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In the present paper, based on the classical Magnus expansion, a simple and efficient fourth-order integrator is given for an arbitrary nonlinear dynamic system, which can preserve the qualitative properties of the exact solution. The proposed method can be considered an averaging technique, and only requires evaluations of exponentials of simple unidimensional integrals. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the method of this paper.

Original language	English
Pages (from-to)	221-228
Number of pages	8
Journal	Mechanics Research Communications
Volume	31
Issue number	2
DOIs	https://doi.org/10.1016/j.mechrescom.2003.10.004
State	Published - Mar 2004

Keywords

Integrator
Magnus expansion
Nonlinear dynamic system

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10.1016/j.mechrescom.2003.10.004

Cite this

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abstract = "In the present paper, based on the classical Magnus expansion, a simple and efficient fourth-order integrator is given for an arbitrary nonlinear dynamic system, which can preserve the qualitative properties of the exact solution. The proposed method can be considered an averaging technique, and only requires evaluations of exponentials of simple unidimensional integrals. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the method of this paper.",

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AB - In the present paper, based on the classical Magnus expansion, a simple and efficient fourth-order integrator is given for an arbitrary nonlinear dynamic system, which can preserve the qualitative properties of the exact solution. The proposed method can be considered an averaging technique, and only requires evaluations of exponentials of simple unidimensional integrals. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the method of this paper.

KW - Integrator

KW - Magnus expansion

KW - Nonlinear dynamic system

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VL - 31

SP - 221

EP - 228

JO - Mechanics Research Communications

JF - Mechanics Research Communications

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ER -

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

Abstract

Keywords

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