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计算数学  2015 

守恒型扩散方程非线性离散格式的性质分析和快速求解

, PP. 227-246

Keywords: 守恒型扩散方程,非线性全隐离散格式,二阶时间精度,存在唯一性,迭代加速

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Abstract:

对于守恒型扩散方程,研究其二阶时间精度非线性全隐有限差分离散格式的性质,证明了其解的存在唯一性.研究了二阶时间精度的Picard-Newton迭代格式,证明了迭代解对原问题真解的二阶时间和空间收敛性,以及对非线性离散解的二次收敛速度,实现了非线性问题的快速求解.本文中方法也适用于一阶时间精度格式的分析,并可推广至对流扩散问题.数值实验验证了二阶时间精度Picard-Newton迭代格式的高精度和高效率.

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