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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Compact stencil ： ウィキペディア英語版 Compact stencil In mathematics, especially in the areas of numerical analysis called numerical partial differential equations, a compact stencil is a type of stencil that uses only nine nodes for its discretization method in two dimensions. It uses only the center node and the adjacent nodes. For any structured grid utilizing a compact stencil in 1, 2, or 3 dimensions the maximum number of nodes is 3, 9, or 27 respectively. Compact stencils may be compared to non-compact stencils. Compact stencils are currently implemented in many partial differential equation solvers, including several in the topics of CFD, FEA, and other mathematical solvers relating to PDE's.〔W. F. Spotz. High-Order Compact Finite Difference Schemes for Computational Mechanics. PhD thesis, University of Texas at Austin, Austin, TX, 1995.〕〔Communications in Numerical Methods in Engineering, Copyright © 2008 John Wiley & Sons, Ltd.〕 ==Two Point Stencil Example== The two point stencil for the ''first derivative'' of a function is given by: $$ f'(x_0)=\frac + O\left(h^2\right) . This is obtained from the Taylor series expansion of the first derivative of the function given by: $\backslash begin$ f'(x_0)=\frac -\frach - \frach^2 - \frach^3 + \cdots \end. Replacing $h$ with $-h$, we have: $\backslash begin$ f'(x_0)=-\frac + \frach - \frach^2 + \frach^3 + \cdots \end. Addition of the above two equations together results in the cancellation of the terms in odd powers of $h$: $\backslash begin$ 2f'(x_0)= \frac -\frac -2\frach^2 + \cdots \end. $\backslash begin$ f'(x_0)= \frac - \frach^2 + \cdots \end. $\backslash begin$ f'(x_0)= \frac + O\left(h^2\right) \end. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Compact stencil」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.