Research PaperNo Access

A high efficiency Lie derivative algorithm for the nonautonomous nonlinear systems

W. A. Jiang

Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China

E-mail Address: wajiang@ujs.edu.cn

Corresponding author.

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Z. H. Gu

Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China

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C. Liu

College of Physics, Liaoning University, Shenyang 110036, P. R. China

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H. R. Feng

College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350002, P. R. China

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, and

L. Q. Chen

Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China

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https://doi.org/10.1142/S0129183123501528Cited by:2 (Source: Crossref)

Abstract

Numerical procedure plays a key role in tackling the solutions of nonlinear dynamical systems. With the advent of the age of big data and high-power computing, developing efficient and fast numerical algorithms is an urgent task. This paper extends the Lie derivative discretization algorithm to the nonautonomous nonlinear systems and investigates the numerical solutions of the systems. The periodic solutions of three different classical nonlinear systems are calculated, and the results are compared to those values calculated from the Runge–Kutta fourth-order algorithm, which demonstrated that the Lie derivative algorithm has the advantages of large time step and short computation time.

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