基于自然边界元的一类拟线性问题的数值算法

基于自然边界归化原理，利用非重叠型区域分解算法（即Dirichlet-Neumann交替算法）研究了长条形区域拟线性方程问题.在得到椭圆人工边界上的自然积分方程后，构造出相应的交替算法，并根据非线性算子的特性，证明了算法在连续和离散条件下的收敛性.数值实例的结果表明，算法是可行且有效的.

Numerical Algorithm for a Class of Quasi Linear Problems Based on Natural Boundary Element Method

Based on the principle of natural boundary reduction,the non overlapping domain decomposition algorithm (Dirichlet-Neumannalternating algorithm) is used to study the quasi linear equations in the long strip region.First,the natural integral equation on the elliptical artificial boundary is obtained;and then,the corresponding iterative algorithm is constructed.According to the characteristics of nonlinear operators,the convergence of the algorithm in continuous and discrete cases is proved,and the corresponding numerical examples are given to illustrate the feasibility of the method.