翻訳と辞書 Words near each other ・ Gaussiran Glacier ・ Gausson ・ Gausson (physics) ・ Gauss–Boaga projection ・ Gauss–Bonnet gravity ・ Gauss–Bonnet theorem ・ Gauss–Codazzi equations ・ Gauss–Hermite quadrature ・ Gauss–Jacobi quadrature ・ Gauss–Kronrod quadrature formula ・ Gauss–Krüger coordinate system ・ Gauss–Kuzmin distribution ・ Gauss–Kuzmin–Wirsing operator ・ Gauss–Laguerre quadrature ・ Gauss–Legendre algorithm ・ Gauss–Legendre method ・ Gauss–Lucas theorem ・ Gauss–Manin connection ・ Gauss–Markov ・ Gauss–Markov process ・ Gauss–Markov theorem ・ Gauss–Newton algorithm ・ Gauss–Seidel method ・ Gaustad ・ Gaustad (station) ・ Gaustad Hospital ・ Gaustadalléen (station) ・ Gaustadt ・ Gaustatoppen ・ Gausturm 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 Gauss–Legendre method ： ウィキペディア英語版 Gauss–Legendre method In numerical analysis and scientific computing, the Gauss–Legendre methods are a family of numerical methods for ordinary differential equations. Gauss–Legendre methods are implicit Runge–Kutta methods. More specifically, they are collocation methods based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method based on ''s'' points has order 2''s''. All Gauss–Legendre methods are A-stable. The Gauss–Legendre method of order two is the implicit midpoint rule. Its Butcher tableau is: : The Gauss–Legendre method of order four has Butcher tableau: : The Gauss–Legendre method of order six has Butcher tableau: : || $\backslash tfrac5$ || $\backslash tfrac29\; -\; \backslash tfrac1\; \backslash sqrt$ || $\backslash tfrac5\; -\; \backslash tfrac1\; \backslash sqrt$ |- | style="border-right:1px solid;" | $\backslash tfrac12$ || $\backslash tfrac5\; +\; \backslash tfrac1\; \backslash sqrt$ || $\backslash tfrac29$ || $\backslash tfrac5\; -\; \backslash tfrac1\; \backslash sqrt$ |- | style="border-right:1px solid; border-bottom:1px solid;" | $\backslash tfrac12\; +\; \backslash tfrac1\; \backslash sqrt$ || style="border-bottom:1px solid;" | $\backslash tfrac5\; +\; \backslash tfrac1\; \backslash sqrt$ || style="border-bottom:1px solid;" | $\backslash tfrac29\; +\; \backslash tfrac1\; \backslash sqrt$ || style="border-bottom:1px solid;" | $\backslash tfrac5$ |- | style="border-right:1px solid;" | || $\backslash tfrac5$ || $\backslash tfrac49$ || $\backslash tfrac5$ |} The computational cost of higher-order Gauss–Legendre methods is usually too high, and thus, they are rarely used. == Notes == 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「Gauss–Legendre 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.