解一维抛物方程的差分格式

DIFFERENCE SCHEMES FOR ONE-DIMENSIONAL PARABOLIC EQUATIONS

对于方程(1),已有多种数值解法,可见[1]和[2]。对于有限差分法,一般来说,隐格式精度高,稳定性好。但是,由于时间方向每前进一步需解一带状方程组,因而存储量和计算量较大。显格式虽然精度不高,稳定性要求较苛刻,但存储量和计算量较小。

In this paper, we derive two classes of difference schemes for one-dimensional parabolicequations. They contain a number of well-known difference schemes. By analysing the localtruncated error, we obtain a class of three-level explicit schemes. These schemes are alwaysstable or condtionally stable under very weak condtions. We also obtain a higher order accu-rate threc-level explicit scheme and condition for its stability is given. A numerical exampleis presented.