翻訳と辞書 Words near each other ・ Finistère's 1st constituency ・ Finistère's 2nd constituency ・ Finistère's 3rd constituency ・ Finistère's 4th constituency ・ Finistère's 5th constituency ・ Finistère's 6th constituency ・ Finistère's 7th constituency ・ Finistère's 8th constituency ・ Finitary ・ Finitary relation ・ Finite ・ Finite & Deterministic Discrete Event System Specification ・ Finite and Infinite Games ・ Finite Automata (band) ・ Finite character ・ Finite difference ・ Finite difference coefficient ・ Finite difference method ・ Finite difference methods for option pricing ・ Finite element exterior calculus ・ Finite element limit analysis ・ Finite element machine ・ Finite element method ・ Finite element method in structural mechanics ・ Finite element model data post-processing ・ Finite element updating ・ Finite extensions of local fields ・ Finite field ・ Finite field arithmetic ・ Finite Fourier transform Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Finite difference ： ウィキペディア英語版 Finite difference A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. Today, the term "finite difference" is often taken as synonymous with finite difference approximations of derivatives, especially in the context of numerical methods. Finite difference approximations are finite difference quotients in the terminology employed above. Finite differences have also been the topic of study as abstract self-standing mathematical objects, e.g. in works by George Boole (1860), L. M. Milne-Thomson (1933), and Károly Jordan (1939), tracing its origins back to Isaac Newton. In this viewpoint, the formal calculus of finite differences is an alternative to the calculus of infinitesimals.〔Jordán, op. cit., p. 1 and Milne-Thomson, p. xxi. Milne-Thomson, Louis Melville (2000): ''The Calculus of Finite Differences'' (Chelsea Pub Co, 2000) ISBN 978-0821821077〕 ==Forward, backward, and central differences== Three forms are commonly considered: forward, backward, and central differences.〔〔〔 A forward difference is an expression of the form :$\backslash Delta\_h()(x)\; =\; f(x\; +\; h)\; -\; f(x).\; \backslash$ Depending on the application, the spacing ''h'' may be variable or constant. When omitted, ''h'' is taken to be 1: $\backslash Delta()(x)\; =\; \backslash Delta\_1()(x)$. A backward difference uses the function values at ''x'' and ''x'' − ''h'', instead of the values at ''x'' + ''h'' and ''x'': :$\backslash nabla\_h()(x)\; =\; f(x)\; -\; f(x-h).\; \backslash$ Finally, the central difference is given by :$\backslash delta\_h()(x)\; =\; f(x+\backslash tfrac12h)-f(x-\backslash tfrac12h)~.$ 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「Finite difference」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.