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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 Strang splitting ： ウィキペディア英語版 Strang splitting Strang splitting is a numerical method of solving ordinary differential equations (ODEs). It is named after Gilbert Strang. The essential idea is that a complex ODE can be decomposed into multiple simpler ODEs. Each ODE can be advanced independently, and then the total change would be the sum of all individual changes. To demonstrate this idea, suppose we have an equation of the form : $\backslash frac\; =\; L\_1\; (\backslash mathbf)\; +\; L\_2\; (\backslash mathbf)$ where $L\_1$, $L\_2$ are differential operators. Suppose further that had we dropped either of the differential operators on the right hand side we would be left with equations that were much simpler to solve. : $\backslash frac\; =\; L\_\; (\backslash mathbf)$ If we start from some point $x\_0$ where value of the function is known $\backslash mathbf\backslash left(x\_0\backslash right)$ and advance it to the next point $x\_0+\backslash Delta\; x$ according to the simplified, reduced ODEs, we will get : $\backslash mathbf\; (x\_0+\backslash Delta\; x)\; =\; \backslash exp(L\_\; (\backslash mathbf\; (x\_0)))\; \backslash mathbf\; (x\_0).$ Combining these two advancement operators yields the value of the function at the next point, according to the complete ODE : $\backslash mathbf\; (x\_0+\backslash Delta\; x)\; =\; \backslash exp(L\_1\; (\backslash mathbf(x\_0)))\; \backslash exp(L\_2(\backslash mathbf(x\_0)))\; \backslash mathbf(x\_0).$ == References == * Marlis Hochbruck, Alexander Ostermann, (Time Integration: Splitting Methods ) * Jason Frank, (Splitting Methods ) 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「Strang splitting」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.