杆振动方程的高阶紧致差分格式

The High-Order Compact Difference Schemes for the Rod Equation

利用不同节点处空间导数的线性组合等于函数值线性组合,或者利用方程自身,得到了梁振动方程的3个模板小、精度高的高阶紧致差分格式,通过分析得到它们都是无条件稳定的.最后借助数值算例验证了理论分析的正确性,格式具有非常高的精度.

Three compact difference schemes with small stencil,high-order for the rod equation are proposed. These scheme are based on the idea that the combination of spatial derivative at different nodes equaling to the combination of functions or the original equation itself. These schemes are unconditionally stable by theoretical analysis and numerical experiments. They are of high accuracy.