求解二维污染扩散方程的时空任意阶的三点紧致显格式

通过在泰勒级数展开中运用逐阶迭代的方法,推导出了空间二阶导数任意精度的三点紧致的表达式,并在半高散方程中通过二维扩散方程本身把时间导数转换为空间导数,从而推导出了时空任意阶的三点紧致显格式.数值实验表明,本文格式的精度很高,而且具有使用简单,易于编程的优点,对求解二维污染扩散方程具有很好的应用前景.

A three-point explicit compact difference scheme with arbitrary order of accuracy for the two dimensional pollutant diffusion equation

Based on the successive iterative approach in the Taylor series expansion method,a three-point explicit compact formula with arbitrary order of accuracy for the spatial second order derivative is derived in this paper.With the transformation of the temporal derivative to spatial derivative from the original diffusion equation,a three-point explicit compact difference scheme for the diffusion equation is proposed and it can achieve arbitrary order of accuracy in both space and time.From the numerical test,it is found that the proposed compact scheme is not only simple to implement and economical to use,but also is effective to apply to many theoretical and engineering problems.