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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 Euler method ： ウィキペディア英語版 Euler method In mathematics and computational science, the Euler method is a SN-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book ''Institutionum calculi integralis'' (published 1768–70).〔; 〕 The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. The Euler method often serves as the basis to construct more complex methods. ==Informal geometrical description== Consider the problem of calculating the shape of an unknown curve which starts at a given point and satisfies a given differential equation. Here, a differential equation can be thought of as a formula by which the slope of the tangent line to the curve can be computed at any point on the curve, once the position of that point has been calculated. The idea is that while the curve is initially unknown, its starting point, which we denote by $A\_0,$ is known (see the picture on top right). Then, from the differential equation, the slope to the curve at $A\_0$ can be computed, and so, the tangent line. Take a small step along that tangent line up to a point $A\_1.$ Along this small step, the slope does not change too much, so $A\_1$ will be close to the curve. If we pretend that $A\_1$ is still on the curve, the same reasoning as for the point $A\_0$ above can be used. After several steps, a polygonal curve $A\_0A\_1A\_2A\_3\backslash dots$ is computed. In general, this curve does not diverge too far from the original unknown curve, and the error between the two curves can be made small if the step size is small enough and the interval of computation is finite.〔; 〕 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「Euler 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.