梁振动方程的多辛Runge-Kutta Nystrom算法

Multi-symplectic Runge-Kutta Nystrom methods for vibration equation of beams

针对梁振动方程问题,给出了一个多辛Hamilton形式,利用Runge-Kutta Nystrm算法离散此多辛结构,得到离散多辛守恒律,并求得了一个等价于Runge-Kutta Nystrm积分的新格式,证明了它的稳定性条件。利用数值计算方法验证了理论分析的正确性。

Due to the problem of vibration equation of beams,a multi-symplectic Hamilton form is given,and this multi-symplectic structure is discreted by using Runge-Kutta Nystrm algorithm to obtain the discrete multi-symplectic conservation law.Then a new scheme which is equivalent to the Runge-Kutta Nystrm integral is obtained,and its stability condition is derived.Finally,the validity of the scheme is verified by using the numerical experiments.