翻訳と辞書 Words near each other ・ 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 ・ Finite geometry ・ Finite group 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 method ： ウィキペディア英語版 Finite difference method In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations, in which finite differences approximate the derivatives. FDMs are thus discretization methods. Today, FDMs are the dominant approach to numerical solutions of partial differential equations. == Derivation from Taylor's polynomial == First, assuming the function whose derivatives are to be approximated is properly-behaved, by Taylor's theorem, we can create a Taylor Series expansion :$f(x\_0\; +\; h)\; =\; f(x\_0)\; +\; \backslash frach\; +\; \backslash frach^2\; +\; \backslash cdots\; +\; \backslash frach^n\; +\; R\_n(x),$ where ''n''! denotes the factorial of ''n'', and ''R''''n''(''x'') is a remainder term, denoting the difference between the Taylor polynomial of degree ''n'' and the original function. We will derive an approximation for the first derivative of the function "f" by first truncating the Taylor polynomial: :$f(x\_0\; +\; h)\; =\; f(x\_0)\; +\; f\text{'}(x\_0)h\; +\; R\_1(x),$ Setting, x0=a we have, :$f(a+h)\; =\; f(a)\; +\; f\text{'}(a)h\; +\; R\_1(x),$ Dividing across by ''h'' gives: :$=\; +\; f\text{'}(a)+$ Solving for f'(a): :$f\text{'}(a)\; =\; -$ Assuming that $R\_1(x)$ is sufficiently small, the approximation of the first derivative of "f" is: :$f\text{'}(a)\backslash approx\; .$ 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 method」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.