梁振动方程的高阶紧致数值格式

High-order compact schemes for the vibration equation of beams

基于紧致差分方法,给出了数值求解梁振动方程的4类高阶有限差分格式,这些数值格式在时间方向具有四阶精度,空间方向上分别具有二阶、四阶和六阶精度。这些格式条件稳定,文章分析给出了这4类格式的稳定性条件。数值算例验证了这些格式的精度阶与理论结果一致;此外,数值算例还对长时间解的演化情况进行了数值模拟,结果显示,数值解与精确解吻合度良好。

To solve the vibration equation of beams numerically,based on the compact method,four high-order numerical finite difference schemes are proposed.These schemes are of fourth-order accuracy in time and second-order,fourth-order or sixth-order accuracy in space respectively.These schemes are stable under some conditions,and the conditions are discussed.The accuracy order of these schemes are verified by the numerical experiments,the numerical results are consistent with the theoretical results.In addition,the evolution of the numerical solution for a long time is also simulated numerically by the numerical experiments.The numerical solution shows a close agreement with the exact solution.