A Numerical Method for the Solutions to Nonlinear Dynamic Systems Based on Cubic Spline  Interpolation Functions

LI Peng-zhu; LI Feng-jun; LI Xing; ZHOU Yue-ting

doi:10.3879/j.issn.1000-0887.2015.08.010

Volume 36 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(8): 887-896

LI Peng-zhu, LI Feng-jun, LI Xing, ZHOU Yue-ting. A Numerical Method for the Solutions to Nonlinear Dynamic Systems Based on Cubic Spline Interpolation Functions[J]. Applied Mathematics and Mechanics, 2015, 36(8): 887-896. doi: 10.3879/j.issn.1000-0887.2015.08.010

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A Numerical Method for the Solutions to Nonlinear Dynamic Systems Based on Cubic Spline Interpolation Functions

doi: 10.3879/j.issn.1000-0887.2015.08.010

¹School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, P.R.China;²School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P.R.China

Funds: The National Natural Science Foundation of China(11261024;11472193;11362108)

Received Date: 2014-11-25
Rev Recd Date: 2015-04-27
Publish Date: 2015-08-15

Abstract

Abstract

The cubic spline interpolation function has good convergence, stability and 2nd-order smoothness. A numerical method for the solutions to nonlinear dynamic systems was constructed with the cubic spline interpolation functions. Advantages and disadvantages were compared between this method and the previous numerical methods for nonlinear dynamic systems, with the error estimation conducted in the 2 numerical examples. The results show that the numerical method derived out of the cubic spline interpolation functions has faster convergence rate and higher accuracy than the existing methods, and has good approximation to the analytical solutions to nonlinear dynamic systems.
- nonlinear dynamic system,
- numerical method,
- cubic spline interpolation

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References

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