梁振动方程的三点稳定紧致差分格式

A Three-point Stable and Compact Difference Scheme for the Vibration Equation of Beams

利用Taylor级数展开方法,给出了数值求解梁振动方程的空间3点的稳定紧致有限差分格式,数值格式在时间方向具有2阶精度,空间方向上具有4阶精度,理论上证明了格式是无条件稳定的.数值算例验证了格式的精度阶,与理论结果一致.此外,数值算例模拟了长时间条件下精确解和数值解的演化情况,结果显示,数值解与精确解吻合度良好.

In this work,by using the Taylor series expansion method,a stable and compact finite difference scheme with three-point in space is proposed for solving the vibration equation of beams numerically. The scheme is of second-order accuracy in time and fourth-order accuracy in space respectively, and this scheme is proved to be unconditionally stable. The accuracy order of this scheme is verified by the numerical experiments,the numerical results are consistent with the theoretical results. In addition, the evolution of the exact solution and the numerical solution for a long time is also simulated numerically,the numerical solution shows a close agreement with the exact solution.