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Improved Theoretical and Numerical Approaches for Solving Linear and Nonlinear Dynamic Systems

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Nonlinear Approaches in Engineering Application

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Abstract

Complex dynamic systems are described by differential dynamic equations, mostly nonlinear without closed form analytic solution. To solve them numerically, there are many methods such as Euler’s method, Taylor-series method and Runge-Kutta method, etc., each with advantages and disadvantages. In this chapter, a novel analytical and numerical methodology for the solutions of linear and nonlinear dynamical systems is introduced. The piecewise constant argument method combined with the Laplace transform, makes the new method called Piecewise constant argument-Laplace transform (PL). This method provides better reliability and efficiency for solving coupled dynamic systems. In addition, the numerical solutions of linear and nonlinear dynamic systems can be obtained smoothly and continuously on the entire time range from zero to t. The numerical results of the analytical solution of the method are given and compared with the results of the 4th-order Runge-Kutta (RK4) method, and the accuracy and reliability of the PL method are verified.

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Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Southwest Petroleum University, Chengdu, China

    Fang Pan & Wang Kexin

  2. Petroleum Engineering School, Southwest Petroleum University, Chengdu, China

    Fang Pan

  3. Engineering and the Applied Sciences, University of Regina, Regina, Canada

    Fang Pan, Dai Liming & Wang Luyao

Authors
  1. Fang Pan
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  2. Dai Liming
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  3. Wang Kexin
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  4. Wang Luyao
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Editor information

Editors and Affiliations

  1. Industrial Systems Engineering, University of Regina, Regina, SK, Canada

    Liming Dai

  2. Mechanical and Automotive Engineering, RMIT University, Bundoora, VIC, Australia

    Reza N. Jazar

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Pan, F., Liming, D., Kexin, W., Luyao, W. (2022). Improved Theoretical and Numerical Approaches for Solving Linear and Nonlinear Dynamic Systems. In: Dai, L., Jazar, R.N. (eds) Nonlinear Approaches in Engineering Application. Springer, Cham. https://doi.org/10.1007/978-3-030-82719-9_1

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  • DOI: https://doi.org/10.1007/978-3-030-82719-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-82718-2

  • Online ISBN: 978-3-030-82719-9

  • eBook Packages: EngineeringEngineering (R0)

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