A high efficiency Lie derivative algorithm for the nonautonomous nonlinear systems

W. A. Jiang, Z. H. Gu, C. Liu, H. R. Feng and L. Q. Chen
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W. A. Jiang: Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China
Z. H. Gu: Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China
C. Liu: College of Physics, Liaoning University, Shenyang 110036, P. R. China
H. R. Feng: College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350002, P. R. China
L. Q. Chen: Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 11, 1-10

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.

Keywords: Lie derivative algorithm; nonautonomous; nonlinear systems; high efficiency (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123501528

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