Relations Between Directional Derivatives for Smooth Functions in 2D and 3D spaces
Relations Between Directional Derivatives for Smooth Functions in 2D and 3D spaces
复制标题
2D 和 3D 空间中平滑函数的方向导数之间的关系
DOI：
10.1007/s10255-016-0610-9
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Long-lun Shen
中科院分区：
文献类型：
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作者：
Gui-xia Lv;Long-lun Shen
本文研究了二维和三维空间中光滑函数的方向导数之间的关系。这些关系以方向导数的线性组合形式建立，其系数具有形式简单和结构规律性。利用它们，导出了几种典型微分算子的基于方向导数的表达式。这为进一步研究方向差分有限点法的数值计算奠定了坚实的数学基础。
In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with their coefficients having simple form and structural regularity. By them, expressions based on directional derivatives for some typical differential operators are derived. This builds up a solid mathematical foundation for further study on numerical computation by the finite point method based on directional difference.