对热传导方程近似解在边界附近的变化研究

Study on Variability of the Solution of Heat Equation Near the Boundaries

讨论了初始条件与边界条件不连续的热传导方程第一类初边界问题近似解在边界附近的变化情况.用有限差分方法求上述定界问题的近似解时,发现绝对稳定的差分格式对较大的网比,在边界附近出现振动.在本文中,讨论振动的发生原因及提出控制振动的一种方法并分析该格式的误差、稳定性等问题,得到了较好的结果.

In this paper, the affects of different initial and boundary condition to the numerical solutions were discussed mainly. And some oscillations near point of discontinuity on both the initial and boundary condition even were found by using the unconditionally stable method. Then the reasons of oscillations and new finite difference equations to control the oscillations were put out. At the end, with a number of numerical experiments, we made sure the reliability and accuracy of the result of this scheme.