Analysis on two approaches for high order accuracy finite difference computation
Analysis on two approaches for high order accuracy finite difference computation
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DOI：
10.1016/j.aml.2012.05.003
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发表时间：
2012-12
期刊：
影响因子：
--
通讯作者：
Jun Zhang;Xinyu Geng;Ruxin Dai
中科院分区：
文献类型：
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作者：
Jun Zhang;Xinyu Geng;Ruxin Dai
我们分析了两种提高标准二阶有限差分格式求解一维椭圆偏微分方程精度的方法。它们是四阶紧致差分格式和基于理查森外推技术的四阶格式。我们研究这些方法的截断误差，并评论它们的规律性要求和计算成本。我们提出数值实验来证明我们分析的有效性。
We analyze two approaches for enhancing the accuracy of the standard second order finite difference schemes in solving one dimensional elliptic partial differential equations. These are the fourth order compact difference scheme and the fourth order scheme based on the Richardson extrapolation techniques. We study the truncation errors of these approaches and comment on their regularity requirements and computational costs. We present numerical experiments to demonstrate the validity of our analysis.