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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 Trapezoidal rule (differential equations) ： ウィキペディア英語版 Trapezoidal rule (differential equations) In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals. The trapezoidal rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multistep method. == Method == Suppose that we want to solve the differential equation :$y\text{'}\; =\; f(t,y).$ The trapezoidal rule is given by the formula :$y\_\; =\; y\_n\; +\; \backslash tfrac12\; h\; \backslash Big(\; f(t\_n,y\_n)\; +\; f(t\_,y\_)\; \backslash Big),$ where $h\; =\; t\_\; -\; t\_n$ is the step size.〔; 〕 This is an implicit method: the value $y\_$ appears on both sides of the equation, and to actually calculate it, we have to solve an equation which will usually be nonlinear. One possible method for solving this equation is Newton's method. We can use the Euler method to get a fairly good estimate for the solution, which can be used as the initial guess of Newton's method. 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「Trapezoidal rule (differential equations)」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.