中文摘要：

对四阶杆振动方程构造含参数高精度三层差分格式，当参数满足一定条件时，差分格式稳定，局部截断误差阶数最高可达O（τ^4＋h^8）．数值例子说明该方法对稳定性的分析是正确的．

英文摘要：

A family of high -accurate and three -layer difference schemes with parameters are con- strutted for solving four - order rod vibration equation. These difference schemes are stable when the parameters satisfy a certain condition. The local truncation error can reach the order of O（τ^4＋h^8） as the maximum. The analysis of stability is correct, as illustrated by numerical example.