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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 Method of undetermined coefficients ： ウィキペディア英語版 Method of undetermined coefficients In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain inhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but instead of using a particular kind of differential operator (the annihilator) in order to find the best possible form of the particular solution, a "guess" is made as to the appropriate form, which is then tested by differentiating the resulting equation. For complex equations, the annihilator method or variation of parameters is less time consuming to perform. Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms.〔Ralph P. Grimaldi (2000). "Nonhomogeneous Recurrence Relations". Section 3.3.3 of ''Handbook of Discrete and Combinatorial Mathematics''. Kenneth H. Rosen, ed. CRC Press. ISBN 0-8493-0149-1.〕 ==Description of the method== Consider a linear non-homogeneous ordinary differential equation of the form :$\backslash sum\_^n\; c\_i\; y^\; +\; y^\; =\; g(x)$ :... where $y^$ denotes the i-th derivate of y, and $c\_i$ denotes a function of x The method consists of finding the general homogeneous solution $y\_c$ for the complementary linear homogeneous differential equation :$\backslash sum\_^n\; c\_i\; y^\; +\; y^\; =\; 0,$ and a particular integral $y\_p$ of the linear non-homogeneous ordinary differential equation based on $g(x)$. Then the general solution $y$ to the linear non-homogeneous ordinary differential equation would be :$y\; =\; y\_c\; +\; y\_p.$〔Dennis G. Zill (2001). ''A first course in differential equations - The classic 5th edition.'' Brooks/Cole. ISBN 0-534-37388-7.〕 If $g(x)$ consists of the sum of two functions $h(x)\; +\; w(x)$ and we say that $y\_$ is the solution based on $h(x)$ and $y\_$ the solution based on $w(x)$. Then, using a superposition principle, we can say that the particular integral $y\_p$ is :$y\_p\; =\; y\_\; +\; y\_.$〔 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「Method of undetermined coefficients」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.