对称分类在非线性偏微分方程组边值问题中的应用  

Application of the symmetry classification to the boundary value problem of nonlinear partial differential equations

作　　者：苏道毕力格[1] 王晓民[1] 乌云莫日根[1] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《物理学报》2014年第4期6-12,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11071159;11261034);内蒙古自治区高等学校科学技术研究项目(批准号:NJZY12056)资助的课题~~

摘　　要：研究了微分方程对称分类在非线性偏微分方程组边值问题中的应用.首先,利用偏微分方程(组)完全对称分类微分特征列集算法确定了给定非线性偏微分方程组边值问题的完全对称分类;其次,利用一个扩充对称将非线性偏微分方程组边值问题约化为常微分方程组初值问题;最后,利用龙格-库塔法求解了常微分方程组初值问题的数值解.In this paper, we study the application of the symmetry classification to the boundary value problem of nonli- near partial differential equations. Firstly, by using differential characteristic set algorithm for the complete symmetry classification of partial differential equations, the complete symmetry classification of a given boundary value problem of nonlinear partial differential equations is proposed. Secondly, by using an extended symmetry, the boundary value problem of nonlinear partial differential equations is reduced to an initial value problem of the original differential equations. Finally, we numerically solve the initial value problem of the original differential equations by using Runge- Kutta method.

关 键 词：对称分类 微分特征列集算法 偏微分方程组边值问题 

分 类 号：O175.8[理学—数学]