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2022 | OriginalPaper | Chapter

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

Authors : Fang Pan, Dai Liming, Wang Kexin, Wang Luyao

Published in: Nonlinear Approaches in Engineering Application

Publisher: Springer International Publishing

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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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next chapter Novel Predictor-Corrector Formulations for Solving Nonlinear Initial Value Problems
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Metadata
Title
Improved Theoretical and Numerical Approaches for Solving Linear and Nonlinear Dynamic Systems
Authors
Fang Pan
Dai Liming
Wang Kexin
Wang Luyao
Copyright Year
2022
Book
Nonlinear Approaches in Engineering Application

Print ISBN: 978-3-030-82718-2

Electronic ISBN: 978-3-030-82719-9

Copyright Year: 2022

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