二维半线性椭圆方程边值问题的牛顿迭代法  

Newton Iterative Method for Boundary Value Problems of Two-dimensional Semilinear Elliptic Equations

作　　者：牟行洋 MOU Xing-yang(School of Management,Jianghan Art Vocational College,Qianjiang Hubei 433100,China)

机构地区：[1]江汉艺术职业学院管理学院,湖北潜江433100

出　　处：《淮阴师范学院学报（自然科学版）》2023年第4期302-308,共7页Journal of Huaiyin Teachers College;Natural Science Edition

摘　　要：利用有限元结合牛顿法求解了一类二维半线性椭圆方程边值问题,推导出它的牛顿迭代格式.数值模拟结果表明,此方法在4个非线性函数情形下选择不同基函数,具有易编程实现,数值解稳定,迭代次数少,运行时间短等优点,证明该方法是可行的和有效的.In this paper,the boundary value problem of a class of two-dimensional semilinear elliptic equations is solved by using finite element method and Newton method,and its Newton iteration scheme is derived.The results of numerical simulation show that this method is feasible and effective by choosing different basis functions in the case of four nonlinear functions,which has the advantages of easy programming,stable numerical solution,less iterations,and short running time.

关 键 词：半线性椭圆方程 有限元 迭代 

分 类 号：O175.25[理学—数学]