指数时程差分Runge-Kutta法在非线性高振荡及迟滞系统中的应用

为满足非线性高振荡及迟滞动力系统的高精度数值计算,提出了指数时程差分RungeKutta法;将传统的差分改为积分,构造出了二阶和三阶指数时程差分RungeKutta算法;将指数时程差分法应用于二阶高振荡动力系统、参数激励与强迫激励联合作用下的非线性振动系统以及迟滞非线性系统中,并与传统的RungeKutta法进行了比较;讨论了计算精度和效率.数值计算结果表明,对于非线性动力学系统,二阶指数时程差分RungeKutta法在计算效率和精度上要优于四阶传统RungeKutta法;该方法适合用于非线性动力学系统分析和数值计算的方法,获得的数值解能够揭示系统的本质特性.

Exponential Time Differencing Runge-Kutta Method for Nonlinear Highly Oscillatory System and Nonlinear Hysteretic System

In order to meet numerical calculation with high precision of nonlinear highly oscillatory system and nonlinear hysteretic system, the exponential time differencing Runge-Kutta methods (ETDRK) were presented.The second-order and third-order exponential time differencing Runge-Kutta methods were constructed by using integration instead of traditional difference. The present methods were applied to a second-order highly oscillatory dynamic system,nonlinear oscillation system under combined parametric and forcing excitation and nonlinear oscillation system with hysteretic restoring force. Accuracy and efficiency of numerical solutions were mentioned in the examples by comparing with the traditional Runge-Kutta method. The numerical calculation results show that accuracy and efficiency of the second-order exponential time differencing Runge-Kutta method are better than those of forth-order traditional Runge-Kutta method. So exponential time differencing Runge-Kutta methods are well suitable for the analysis and calculation for the nonlinear dynamic mechanical systems,and the obtained numerical solutions can be used to show the essential characters of the systems.