A Numerical Method for the Solutions to Nonlinear Dynamic Systems Based on Cubic Spline Interpolation Functions
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摘要: 三次样条插值函数具有良好的收敛性、稳定性与二阶光滑性.研究了借助三次样条插值函数构造的非线性动力系统数值求解方法,分析了该方法与已有的非线性动力系统数值求解方法的优缺点,刻画了误差估计且给出了数值算例.结果表明基于三次样条插值函数构造的数值方法比已有的方法收敛速度快、逼近精度高且能够很好地逼近非线性动力系统的解析解.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.
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Key words:
- nonlinear dynamic system /
- numerical method /
- cubic spline interpolation
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