Burgers方程的级数解  

Series Solution to the Burgers' Equation

作　　者：鲁晓莉[1] 赵书博[1] 黄鹏展[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《伊犁师范学院学报（自然科学版）》2015年第2期15-20,共6页Journal of Yili Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(11401511);国家级大学生创新训练计划项目(201410755006)

摘　　要：应用一种解析技巧——同伦分析方法求解了Burgers方程.与之前的工作不同,Burgers方程的求解基于了Hopf-Cole变换方法.通过与先前的方法比较,结果表明同伦分析方法能够有效处理非线性问题,并提供一个方便的方式来控制收敛区域和级数解的收敛率.In this paper,Burgers’equation is solved by an analytic technique named homotopy analysis meth-od. Different from previous work,we solve this equation based on the Hopf-Cole transformation. The comparisons are made among the results of the present work,the previous work and the homotopy perturbation method. It is indi-cated that homotopy analysis method is valid for dealing with the nonlinearity and provides a convenient way of con-trolling the convergence region and rate of the series solution.

关 键 词：BURGERS方程 同伦分析方法 级数解 Hopf-Cole变换 收敛性分析 

分 类 号：O241[理学—计算数学]