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    Title: Numerical traveling wave solutions of some nonlinear mixed-type lattice differential equations
    Other Titles: 某些非線性混合型網格微分方程的行進波之數值解
    Authors: 黃清郎;Huang, Ching-lang
    Contributors: 淡江大學數學學系碩士班
    楊定揮;Yang, Ting-hui
    Keywords: 耦合輪廓方程式;有限差分法;牛頓迭代;連續法;Coupling profile equation;Finite difference method;Continuation method;Newton's iteration
    Date: 2008
    Issue Date: 2010-01-11 02:56:12 (UTC+8)
    Abstract: 我們使用有限差分法來計算二維的網格型微分方程之行進波波前解。特別地,在方程式中非線性的反應函數為雙穩定的類型,且其擴散項具有函數耦合之特性。在特徵方程式的某些適當條件下,我們證明了正向波速的存在性,它能夠幫助我們近似在輪廓方程式邊界上的漸近行為。最後我們將以牛頓法解,由有限差分法所導出之非線性代數方程。在牛頓迭代中,為了克服尋找好的初始解困難,我們採用了參數連續法。
    We present a finite difference method for computing traveling wave front solutions of a two-dimensional lattice differential equations. In particular, the nonlinear reaction function is bi-stable type and the diffusion term is with function-couple. Under some suitable conditions on the characteristic equation, we prove the existence of the positive wave speed. It can help us to approximate the asymptotically behavior on the boundaries of profile equation. Newton''s method is used to find the solution of nonlinear algebraic equations inducing by the finite difference method. To overcome the difficulty of finding a good initial solution of Newton''s iteration, the continuation method is implemented.
    Appears in Collections:[數學學系暨研究所] 學位論文

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