摘要
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.
作者
张静静
邵静芳
李祥贵
ZHANG Jingjing, SHAO Jingfang, LI Xianggui(School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, Chin)
出处
《中国科技论文》
CAS
北大核心
2018年第5期552-557,共6页
China Sciencepaper
基金
国家自然科学基金资助项目(11671044)
国防基础科研科学挑战计划资助项目(TZ2016001)
北京市教育委员会专项项目(PXM2017_014224_000020)
关键词
梁振动方程
紧致格式
有限差分格式
高阶数值格式
vibration equation of beams
compact scheme
finite difference scheme
high-order numerical scheme