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求解二维扩散方程的一种高精度紧致差分格式

DOI: 10.3969/j.issn.1001-8395.2015.03.011, PP. 365-370

Keywords: 扩散方程,四次样条函数,Padé逼近,高精度紧致格式,无条件稳定

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Abstract:

扩散方程通常用来描述扩散现象中的物质密度的变化或者与扩散相类似的现象,针对二维扩散方程提出了一种高精度紧致差分格式,该格式基于四次样条函数对空间变量进行离散,对时间导数采用(2,2)Padé逼近,从而得到了时间和空间均为四阶精度的紧致差分格式.然后证明了该格式是无条件稳定的.最后通过数值实验,验证方法的精确性和稳定性.

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