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Solving Fractional Dynamical System with Freeplay by Combining Memory-Free Approach and Precise Integration Method

Author

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  • Q. X. Liu
  • X. S. He
  • J. K. Liu
  • Y. M. Chen
  • L. C. Huang

Abstract

The Yuan-Agrawal (YA) memory-free approach is employed to study fractional dynamical systems with freeplay nonlinearities subjected to a harmonic excitation, by combining it with the precise integration method (PIM). By the YA method, the original equations are transformed into a set of first-order piecewise-linear ordinary differential equations (ODEs). These ODEs are further separated as three linear inhomogeneous subsystems, which are solved by PIM together with a predictor-corrector process. Numerical examples show that the results by the presented method agree well with the solutions obtained by the Runge-Kutta method and a modified fractional predictor-corrector algorithm. More importantly, the presented method has higher computational efficiency.

Suggested Citation

  • Q. X. Liu & X. S. He & J. K. Liu & Y. M. Chen & L. C. Huang, 2016. "Solving Fractional Dynamical System with Freeplay by Combining Memory-Free Approach and Precise Integration Method," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-7, April.
    • Handle: RePEc:hin:jnlmpe:9430528
    DOI: 10.1155/2016/9430528
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