A Numerical Approximation Method for Solutions to Nonlinear Dynamic Systems Based on Multiquadric Quasi-Interpolation Functions

DU Shan; LI Feng-jun

doi:10.21656/1000-0887.370368

Volume 38 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(8): 943-955

DU Shan, LI Feng-jun. A Numerical Approximation Method for Solutions to Nonlinear Dynamic Systems Based on Multiquadric Quasi-Interpolation Functions[J]. Applied Mathematics and Mechanics, 2017, 38(8): 943-955. doi: 10.21656/1000-0887.370368

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A Numerical Approximation Method for Solutions to Nonlinear Dynamic Systems Based on Multiquadric Quasi-Interpolation Functions

doi: 10.21656/1000-0887.370368

School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China(11261024；61662060)

Received Date: 2016-11-29
Rev Recd Date: 2017-01-13
Publish Date: 2017-08-15

Abstract

Abstract

The multiquadric quasi-interpolation function has advantages of high accuracy and good stability. A new numerical method for resolving the initial value problems of nonlinear dynamic systems was proposed via combination of the multiquadric quasi-interpolation function and the 4th-order Runge-Kutta method. The advantages and disadvantages were analyzed between this new method and the existing numerical methods for nonlinear dynamic systems, according to the numerical example and error estimation. The results show that the proposed method needs less computation cost and enables fine approximation to the analytical solutions to nonlinear dynamic systems.
- nonlinear dynamic system,
- numerical method,
- multiquadric quasi-interpolation,
- 4th-order Runge-Kutta method

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References

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