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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 FTCS scheme ： ウィキペディア英語版 FTCS scheme In numerical analysis, the FTCS (Forward-Time Central-Space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations. It is a first-order method in time, explicit in time, and is conditionally stable when applied to the heat equation. When used as a method for advection equations, or more generally hyperbolic partial differential equation, it is unstable unless artificial viscosity is included. The abbreviation FTCS was first used by Patrick Roache. ==The method== The FTCS method is based on central difference in space and the forward Euler method in time, giving first-order convergence in time and second-order convergence in space. For example, in one dimension, if the partial differential equation is :$\backslash frac\; =\; F\backslash left(u,\; x,\; t,\; \backslash frac\backslash right)$ then, letting $u(i\; \backslash ,\backslash Delta\; x,\; n\backslash ,\; \backslash Delta\; t)\; =\; u\_^\backslash ,$, the forward Euler method is given by: :$\backslash frac\; -\; u\_^\}\; =$ F_^\left(u, x, t, \frac\right) The function $F$ must be discretized spatially with a central difference scheme. This is an explicit method which means that, $u\_^$ can be explicitly computed (no need of solving a system of algebraic equations) if values of $u$ at previous time level $(n)$ are known. FTCS method is computationally inexpensive since the method is explicit. 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「FTCS scheme」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.