這篇論文主要在研究網格型微分方程的行進波的數值解。我們利用指數型遞減去逼進有限區間之外的行進解，在有限區間之內我們利用有限差分逼進解的一階微分項以及利用continuation method 去逼近輸出函數 。然後再利用牛頓法去疊代找出行進波的數值解。在論文的最後一節我們也給了一些數值圖形去驗證行進波解的存在性。

In this thesis, we investigate a numerical method for solving nonlinear differential-difference equations arising from the traveling wave equations of a large class of lattice di®erential equations. The pro¯le equation is
of ¯rst order with asymptotically boundary conditions. The problem is approximated via a difference scheme which solves the problem on a finite interval by applying an asymptotic representation at the endpoints and iterative techniques to approximate the speed, and a continuation method to start the procedure. The procedure is tested on a class of problems
which can be solved analytically to access the scheme''s accuracy and stability, and applied to many lattice differential equations that models
the waves propagation in neural networks.

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