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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 Partial differential algebraic equation ： ウィキペディア英語版 Partial differential algebraic equation In mathematics a partial differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set of algebraic equations. == Definition == A general PDAE is defined as: : $0\; =\; \backslash mathbf\; F\; \backslash left(\; \backslash mathbf\; x,\; \backslash mathbf\; y,\; \backslash frac,\; \backslash frac,\; \backslash ldots,\; \backslash mathbf\; z\; \backslash right),$ where: * F is a set of arbitrary functions; * x is a set of independent variables; * y is a set of dependent variables for which partial derivatives are defined; and * z is a set of dependent variables for which no partial derivatives are defined. The relationship between a PDAE and a partial differential equation (PDE) is analogous to the relationship between an ordinary differential equation (ODE) and a differential algebraic equation (DAE). PDAEs of this general form are challenging to solve. Simplified forms are studied in more detail in the literature.〔Wagner, Y. 2000. "A further index concept for linear PDAEs of hyperbolic type," Mathematics and Computers in Simulation, v. 53, pp. 287–291.〕〔W. S. Martinson, P. I. Barton. (2002) "Index and characteristic analysis of linear PDAE systems," Siam Journal on Scientific Computing, v. 24, n. 3, pp. 905–923.〕〔Lucht, W.; Strehmel, K.. 1998. "Discretization based indices for semilinear partial differential algebraic equations," Applied Numerical Mathematics, v. 28, pp. 371–386.〕 Even as recently as 2000, the term "PDAE" has been handled as unfamiliar by those in related fields.〔Simeon, B.; Arnold, M.. 2000. "Coupling DAEs and PDEs for simulating the interaction of pantograph and catenary," Mathematical and Computer Modelling of Dynamical Systems, v. 6, pp. 129–144.〕 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「Partial differential algebraic equation」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.