          下載電子全文 （限經由淡江IP使用）
 系統識別號 U0002-2607201121440200 中文論文名稱 延續法解泛函微分方程 英文論文名稱 A Continuation Method for Solution of Functional Differential Equation 校院名稱 淡江大學 系所名稱(中) 數學學系碩士班 系所名稱(英) Department of Mathematics 學年度 99 學期 2 出版年 100 研究生中文姓名 曾群雄 研究生英文姓名 Qun-Xiong Ceng 學號 696190023 學位類別 碩士 語文別 英文 口試日期 2011-06-24 論文頁數 17頁 口試委員 指導教授-楊定揮委員-許正雄委員-楊智烜 中文關鍵字 延續 英文關鍵字 Runge-Kutta  collocation  continuation  functional differential equation  traveling wave  reaction-diffusion equation  bistable  delay  advance  mixtype 學科別分類 學科別＞自然科學＞數學 中文摘要 對於此次的研究中，針對解決離散空間上的反應擴散方程行進波問題。首先使用基於隱型Runge-Kutta演算程序(Implicit Runge-Kutta)、配置法則(Collocation Method) 等泛函微分方程(Functional Differential Equations, FDE)技巧，以上述數值計算方法處理典型 bistable型離散空間上的反應擴散方程。其中包含以延續法(Continuation Method)之數值技巧作為解決行進波問題的對策。並在文章最後列舉兩個實際實驗結果的呈現。 英文摘要 In this work, traveling wave solutions for reaction-diffusion equations on a discrete spatial domain are considered. We use the collocation method based on k-stage implicit Runge-Kutta scheme to compute numerically the functional differential equation which is the profile equation of some typical bistable spatial discrete reaction diffusion equation. Numerical techniques for solving the traveling wave equations include the continuation method. Finally, some numerical results are presented. 論文目次 1 Introduction 1 2 Preliminaries 2 2.1 Implicit Runge-Kutta Scheme and Collocation Method . . . . 2 2.2 The linear case . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Qusilinearization for Nonlinear Case . . . . . . . . . . . . . . . 6 3 Applications : Traveling Wave Solution Problems 7 3.1 Boundary Functions and Boundary Conditions . . . . . . . . . 8 3.2 DDE Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4 Numerical Results 12 5 Conclusions 13 參考文獻  Kate A Abell, Christopher E Elmer, A. R Humphries, and Erik S Van Vleck, Computation of mixed type functional di?erential boundary value problems,SIAMJ.Appl.Dyn.Syst.4(2005),no.3,755–781(electronic).  Paolo Arena, Maide Bucolo, Stefano Fazzino, Luigi Fortuna, and Mattia Frasca, The cnn paradigm: shapes and complexity, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005), no. 7, 2063–2090.  PeterWBatesandAdamChmaj, A discrete convolution model for phase transitions, Arch. Ration. Mech. Anal. 150 (1999), no. 4, 281–305.  Jonathan Bell, Some threshold results for models of myelinated nerves, Math. Biosci. 54 (1981), no. 3-4, 181–190.  Henjin Chi, Jonathan Bell, and Brian Hassard, Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory, J. Math. Biol. 24 (1986), no. 5, 583–601.  Leon O Chua, Cnn: a vision of complexity, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 7 (1997), no. 10, 2219–2425.  LeonOChua,MartinHasler, GeorgeSMoschytz, andJacquesNeirynck, Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation, IEEE Trans. Circuits Systems I Fund. Theory Appl. 42 (1995), no. 10, 559–577.  Christopher E Elmer and Erik S Van Vleck, Computation of traveling waves for spatially discrete bistable reaction-diffusion equations, Appl. Numer. Math. 20 (1996), no. 1-2, 157–169.  Christopher E Elmer and Erik S Van Vleck,Analysis and computation of travelling wave solutions of bistable differential-di?erence equations, Nonlinearity 12 (1999), no. 4, 771–798.  Christopher E Elmer and Erik S Van Vleck, A variant of newton’s method for the computation of traveling waves of bistable di?erential-di?erence equations, Journal of Dynamics and Differential Equations 14 (2002), no. 3, 493–517.  Thomas Erneux and Gr’egoire Nicolis, Propagating waves in discrete bistable reaction-di?usion systems, Phys. D 67 (1993), no. 1-3, 237–244.  James Keener and James Sneyd, Mathematical physiology. vol. i: Cel- lular physiology, 8/ (2009), xxvi+470+A2+R45+I29.  , Mathematical physiology. vol. ii: Systems physiology, 8/(2009), i–xxvi, 471–974, A1–A2, R1–R45 and I1–I29. 論文使用權限 同意紙本無償授權給館內讀者為學術之目的重製使用，於2011-07-28公開。同意授權瀏覽/列印電子全文服務，於2011-07-28起公開。 若您有任何疑問，請與我們聯絡！圖書館： 請來電 (02)2621-5656 轉 2486 或 來信 