Numerical Computation for Traveling Wave Solutions of Lattice Differential Equations

• Main Authors: Yi-Chun Lin, 林意淳
• Other Authors: Cheng-Hsiung Hsu
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/35005857248522363461

碩士 === 國立中央大學 === 數學研究所 === 93 === 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.