含高阶余项的非线性动力系统数值计算法

A high-precision numerical method for non-linear dynamic systems

建立了一种求解非线性动力系统高精度数值计算的新方法,重构了等价的非线性动力系统方程,该方程考虑了非线性函数的任意高阶项,并给出了该方程的Duhamel积分表达式,在时间步长内用Newton-Raphson法进行数值迭代求解,该方法能连续满足微分方程而不只是在离散的步长端点满足方程,从而打破了传统的Euler型有限差分法。计算实例表明,该方法计算精度高于传统的Runge-Kutta,Newmark-β和Wilson-θ等方法。

A new high-precision numerical arithmetic for solving the non-linear dynamic system is proposed.The ordinary nonlinear dynamic equation is reconstructed,and the new equivalent equation taining arbitrary high order remainder.The arithmetic presents Duhamel integration expression,using Newton-Raphson iterative arithmetic to seek the numerical solution,satisfying the differential equation continuously rather than at discrete spots,therefore,the arithmetic exceeds the traditional Euler finite differential method.Compared with the traditional method,such as Runge-Kutta method,Newmark-β method and Wilson-θ et al.,the calculation precision of this method is much higher.