一类振动Timoshenko梁方程组的二阶差分格式

摘要

In this paper, we derive a linear three-level difference scheme for a vibrating Timoshenko beam equations by the method of reduction of order on uniform meshes and have proved that the scheme is uniquely solvable, unconditionally stable and second order convergent in L∞ norm with the discrete energy method. The result of the theoretical analysis is verified experimentally.%本文用降阶法技巧对一类振动Timoshenko梁方程组构造了一个三层线性差分格式,用能量分析方法证明了格式的唯一可解性,无条件稳定性和在L∞范数下的二阶收敛性.最后给出了数值例子验证了理论结果.