求解扩散方程的高精度显式紧致差分格式

High accuracy explicit compact difference scheme for the diffusion equation

首先针对一维扩散方程,空间方向采用二阶导数的四阶紧致差分公式进行离散,时间方向采用泰勒级数展开的方法进行离散,推导出了一种高精度显式紧致差分格式;然后通过Fourier分析方法给出了格式的稳定性条件为λ≤1/2(λ为网格比);最后通过数值实验验证了格式的精确性和可靠性.

Based on the fourth-order compact difference formula of the second-order derivative in spatialdirection and Taylor series expansion in time direction,a high-order explicit compact difference scheme forthe one dimentional diffusion equation is developed. The stability of the scheme is analyzed by Fouriermethod,and the condition of stability is λ≤1/2. （λis the mesh ratio）. Numerical experiments are carried outto verify the accuracy and reliability of the present scheme.