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

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.