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標題: The blow-up problem while using the Crank-Nicolson scheme
使用 Crank-Nicolson 方法的爆炸問題
作者: 陳偉淵
Wei -Yuan Chen
引用: [1] Y.-G. CHEN , Asympeotic behaviours of blowing-up solutions for finite difference analogue of ut = uxx + u1+α , J. Fac. Sci. Univ . Tokyo Sect. IA , 33(1986) , pp. 541-574. [2] TSUTSUMI , M., Existence and nonexistence of global solutions for nonlinear parabolic equa- tions, Publ.Res. Inst. Math. Sci 8 (1972) ,211-229. [3] TSUTSUMI , M., Existence and nonexistence of global solutions of the first boundary problem for a certain quasilinear parabolic equation , Funkcial . Ekvac. 17 (1974) , 13-24. [4] C-H. CHO, On a finite difference shceme for the parabolic blow-up problems , Master's Thesis , Research Institute for Mathematical Science ,Kyoto university (2005). [5] C-H. CHO and HISASHI OKAMOTO ,Further remarks on asymptotic behavior of the numer- ical solutions of parabolic blow up problems , (207),213-226. [6] NAKAGAWA , T., Blowing up of a finite difference solution to ut = uxx + u2 , Appl. Math . Optim. 2 (1976) , 337-350. [7] FRED B.WEISSLER , Single point blow-up of semilinear initial vaulue problems , J. Diff. Eqns ., 55 (1984) , pp. 202-224.
摘要: In this thesis, we investigate some properties of of solutions of difference equations. In particular, we consider the Crank-Nicolson schemes for various parabolic partial differential equations. The blow up problem for the Crank-Nicolson scheme should be discussed in this paper.
在這篇論文中,我們研究差分方程式的解的一些性質。特別是,我們考慮 Crank-Nicolson的 差 分 方 程 式 應 用 在 各 種 拋 物 型 偏 微 分 方 程 。 有 關 Crank-Nicolson差分方程式的爆破問題會在本文中討論。
文章公開時間: 10000-01-01
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