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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
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[8] Christopher E Elmer and Erik S Van Vleck, Computation of traveling
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