热传导方程差分解法的最佳网格

The Best Mesh of the Difference Solution of the Heat-conduction Equation

论述了用有限差分方法求解一维热传导方程带权六点格式的最优网格选择问题,即在固定的运算次数下,对给定的权系数一,如何选择空间步长△x与时间步长△t,使得在此网格下,六点格式有更高阶的截断误差,并且保持差分解的正性。

This article discusses the method of finite difference to solve the selection problem of the optimal mesh about one-dimensional heat-conduction equation, weight with six formats, that is how to choose the space step △x and time step △t under at the condition of the fixed operation degree and the given weight coefficient θ in order to make the six formats own the higher truncation error and keep the difference solution positive property under this mesh.