(3.237.20.246) 您好!臺灣時間:2021/04/15 18:48
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:胡昶偉
研究生(外文):Chang-Wei Hu
論文名稱:關於半線性熱方程的數值爆炸集合
論文名稱(外文):On the Numerical Blow-up Set for the Semilinear Heat Equation
指導教授:卓建宏卓建宏引用關係
指導教授(外文):Chien-Hong Cho
口試委員:林敏雄洪宗乾
口試日期:2014-07-24
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:18
外文關鍵詞:Numerical Blow-up SetSemilinear Heat Equation
相關次數:
  • 被引用被引用:0
  • 點閱點閱:95
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:7
  • 收藏至我的研究室書目清單書目收藏:0
我們考慮對於半線性熱方程和其非負初始質以及Dirichlet邊界條件的有限差分近似. 我們知道,雖然半線性熱方程在有限時間爆炸是可以有方法和使用適當的時間網格去證明,但在數值爆炸集合方面卻不一定會與真實的一致. 而在這篇文章中, 我們的目的是使用不同的時間網格來尋找數值爆炸集合.
We consider the finite difference approximation for the semilinear heat equation
u_t = u_xx+f(u) (0 < t; 0 < x < 1) with nonnegative initial data u(0, x) = u_0(x) (0 < x < 1) and the Dirichlet boundary condition u(t, 0) = u(t, 1) = 0 (t > 0). It is known that although the finite-time blow-up for the semilinear heat equation can be reproduced by a scheme with adaptively-defined time mesh, the numerical blow-up
sets do not always coincide with that of the real one. In this paper, we are aimed to investigate the numerical blow-up sets with respect to different time meshes.
1 Introduction 2
2 Explicit scheme 5
3 Implicit scheme 11
4 Conclusion 15
5 References 16
[1] C.-H. Cho, On the Computation of the Numerical Blow-up Time. Method Partial Dif-
ference. To appear in Japan J. Indust. Appl. Math.
[2] C.-H. Cho, S. Hamada and H. Okamoto, On the Finite Di erence Approximation for a
Parabolic Blow-up Problem. Japan J. Appl. Math. 24 (2007), 475-498.
[3] C.-H. Cho and H. Okamoto, Further Remerks on Asymptotic Behavior of the Numerical
Solutions of the Parabolic Blow-up Problems. Meth. Appl. Anal. 14 (2007), 213-226.
[4] Nakagawa, T., Blowing up of a Finite Di erence Solution to ut = uxx+u2. Appl. Math.
Optim. 2 (1976), 337-350.
[5] Y.-G. Chen, Asymptotic Behaviours of Blowing-up Solutions for Finite Di erence Ana-
logue of ut = uxx + u1+ . J. Fac. Sci., Univ. Tokyo 33 (1986), 541-574.
[6] P. Groisman, Totally Discrete Explicit and Semi-implicit Euler methods for a Blow-up
Problem in Several Space Dimensions. Computing, 76 (2006), 325-352.
[7] C.-F. Chang, A Finite Di erence Scheme for Blow-up Solutions of the Convective
Reaction-di usion Eequations. Math Thesis.
[8] T.-F. Chen, Levine H. A., and Sacks P. E.: Analysis of a convective reaction-di usion
equation. Nonlinear Anal. Theor. Meth. Appl. 12, (1988), 1394-1370.
[9] K. Deng and H.A Levine, The Role of Critical Exponents in Blow-up Theorems: The
Sequal, J. Math. Anal. Appl., 243 (2000), pp. 85-126.
[10] A. Friedman and B. BcLeod, Blow-up of Positive Solutions of Semilinear Heat Equa-
tions, Indiana Univ. Math. J., 34 (1985), pp. 425-447.
[11] S. Ito, On Blow-up of Positive Solutions of Semilinear Parabolic Equations, J. Fac. Sci.
Univ. Tokyo, Sect. IA, 37 (1990), pp. 527-536
[12] L.Abia, J.C. Lopez-Marcos, J. Martnez, The Euler method in the numerical integration
of reaction-di usion problem with blow-up, Appl. Numer. Math., 38 (2001) 287-313.
17
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔