一类Timoshenko梁方程组的二阶差分格式

A Second-order Difference Scheme for a Timoshenko Beam Equations

用降阶法技巧对一类Timoshenko梁方程组构造了三层线性差分格式,并用能量分析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。最后举例说明了该理论的应用。

In this study, we derive a finite difference for a Timoshenko beam with boundary feedback by the method of reduction of order on uniform meshes. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable andsecond order convergent in L∞ norm. Numerical results demonstrate the theoretical results.