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。

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.

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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