一类抛物型偏微分方程的特征中心差分方法

摘要

运用特征中心差分方法来求解一类抛物型偏微分方程。通过对网格的不均匀剖分来离散方程，得到方程的特征中心差分格式。作了 H1误差估计，给出了相应的定理。数值实验表明该方法对解此类问题是高效稳定的%　　In this paper, we develop a new characteristic centered difference method for a class of parabolic partial differential equations. We adopt the non-uniform subdivision for the equation. Then the error estimates of H1-norm is obtained. At last, a numerical experiment is presented to illustrate that the accuracy of this method is higher, the scheme is effective, and the method is suitable for solving this problem.