基于搜索延拓的多启动参数微分法求解非线性微分方程多解问题  

The Multi-Starting Parameter Differential Method Based on Search Extension for Solving Multiple Solutions of Nonlinear Differential Equations

作　　者：李璨[1] 刘跃武[1] 谢资清[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,中国长沙410081

出　　处：《湖南师范大学自然科学学报》2008年第1期14-18,共5页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(10571053);湖南省教育厅优秀青年资助项目(05B039)

摘　　要：基于搜索延拓法,结合参数微分法,计算出了立方非线性问题Δu+u3=0在Ω内,u=0在Ω上的多个解,减少了计算量,缩短了计算时间,并通过数值例子证实了该方法的有效性.In order to solve the multiple solutions of cubic nonlinear differential equations, i.e. △u ＋ u^3 =0,inΩ; u =0, on αΩ, the method＇s efficiency has been improved based on search extension method and parameter differential method. The computation time has been reduced and the computation speed has been improved. The numerical results are presented to show the efficiency of the method.

关 键 词：参数微分法 搜索延拓法 非线性微分方程 多解 

分 类 号：O242.21[理学—计算数学]