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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 Backward differentiation formula ： ウィキペディア英語版 Backward differentiation formula The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations. They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed times, thereby increasing the accuracy of the approximation. These methods are especially used for the solution of stiff differential equations. == General formula == A BDF is used to solve the initial value problem : $y\text{'}\; =\; f(t,y),\; \backslash quad\; y(t\_0)\; =\; y\_0.$ The general formula for a BDF can be written as : $\backslash sum\_^s\; a\_k\; y\_\; =\; h\; \backslash beta\; f(t\_,\; y\_),$ where $h$ denotes the step size and $t\_n\; =\; t\_0\; +\; nh$. The coefficients $a\_k$ and $\backslash beta$ are chosen so that the method achieves order $s$, which is the maximum possible. BDF methods are implicit and, as such, require the solution of nonlinear equations at each step. Typically, a modified Newton's method is used to solve these nonlinear equations.〔 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「Backward differentiation formula」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.