The Continuation of Solution Paths for The Brusselator Model with Multiple Parameters

• Main Authors: ＬＩＵ ＴＳＵＮＧ ＣＨＩ, 劉中吉
• Other Authors: 簡國清
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/20207229265375286654

碩士 === 國立新竹教育大學 === 進修部數理教育碩士班(數學組) === 93 === In this thesis, we will investigate the continuation of solution paths for the Brusselator model. We ues the central difference method to investigate the multiple solution paths of the Brusselator model. Moreover, we investigate a Brusselator model to find solution paths containing bifurcation points, turning points and regular points of the Brusselator model. It will be helpful to understand the qualitative properties in the solutions of the Brusselator model. In this paper, we apply implicit function theorem, central difference method, Newton’s iterative method, secant predictor method, pseudo–arclength continuation method to find the solution paths of the Brusselator model. At the same time, we use numerical methods to find solution paths containing bifurcation points, turning points and regular points and use proper iterative methods to analysis and investigate the continuation of solution paths for the Brusselator model.