Numerical Traveling Wave Solutions of Some Nonlinear Mixed-type Lattice Differential Equations

• Main Authors: Ching-Lang Huang, 黃清郎
• Other Authors: Ting-Hui Yang
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/40101792338233423003

碩士 === 淡江大學 === 數學學系碩士班 === 96 === 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.