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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 shooting method ： ウィキペディア英語版 shooting method In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to the solution of an initial value problem. The following exposition may be clarified by this illustration of the shooting method. For a boundary value problem of a second-order ordinary differential equation, the method is stated as follows. Let :$y\text{'}\text{'}(t)\; =\; f(t,\; y(t),\; y\text{'}(t)),\; \backslash quad\; y(t\_0)\; =\; y\_0,\; \backslash quad\; y(t\_1)\; =\; y\_1$ be the boundary value problem. Let ''y''(''t''; ''a'') denote the solution of the initial value problem :$y\text{'}\text{'}(t)\; =\; f(t,\; y(t),\; y\text{'}(t)),\; \backslash quad\; y(t\_0)\; =\; y\_0,\; \backslash quad\; y\text{'}(t\_0)\; =\; a$ Define the function ''F''(''a'') as the difference between ''y''(''t''1; ''a'') and the specified boundary value ''y''1. :$F(a)\; =\; y(t\_1;\; a)\; -\; y\_1\; \backslash ,$ If ''F'' has a root ''a'' then obviously the solution ''y''(''t''; ''a'') of the corresponding initial value problem is also a solution of the boundary value problem. Conversely, if the boundary value problem has a solution ''y''(''t''), then ''y''(''t'') is also the unique solution ''y''(''t''; ''a'') of the initial value problem where ''a = y'''(''t''0), thus ''a'' is a root of ''F''. The usual methods for finding roots may be employed here, such as the bisection method or Newton's method. == Linear shooting method == The boundary value problem is linear if ''f'' has the form :$f(t,\; y(t),\; y\text{'}(t))=p(t)y\text{'}(t)+q(t)y(t)+r(t).\; \backslash ,$ In this case, the solution to the boundary value problem is usually given by: :$y(t)\; =\; y\_(t)+\backslash frac(t\_1)\}y\_(t)$ where $y\_(t)$ is the solution to the initial value problem: :$y\_\text{'}\text{'}(t)\; =\; p(t)y\_\text{'}(t)+q(t)y\_(t)+r(t),\backslash quad\; y\_(t\_0)\; =\; y\_0,\; \backslash quad\; y\_\text{'}(t\_0)\; =\; 0,$ and $y\_(t)$ is the solution to the initial value problem: :$y\_\text{'}\text{'}(t)\; =\; p(t)y\_\text{'}(t)+q(t)y\_(t),\backslash quad\; y\_(t\_0)\; =\; 0,\; \backslash quad\; y\_\text{'}(t\_0)\; =\; 1.$ See (the proof ) for the precise condition under which this result holds. 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「shooting 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.