一类边界积分方程的高精度机械求积法  

High Accuracy Mechanical Quadrature Method for Solving Boundary Integral Equations

作　　者：程攀[1] 黄晋[1] 王前东[1] 吕涛[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2004年第6期1109-1115,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10171073)

摘　　要：提出了解非线性边值问题的边界积分方程的高精度机械求积法.积分算子被分解成单调的Hammerstein算子和一个紧算子后,运用Sidi求积公式,建立了非线性离散方程组.并借助Anselone的渐近紧收敛理论和Stepleman定理,证明了离散方程组的解存在性、惟一性、收敛性和精度阶O(h3).使用Ostrowski的不动点定理,提供了三阶收敛的迭代法.数值试验说明了该方法的可靠性.In this paper, the authors present mechanical quadrature methods for solving the boundary integral equations of nonlinear boundary value problems. After the boundary integral operator is decomposed into the sum of a monotonous Hammerstein operator and a compact mapping by the Sidi rule, they construct the nonlinear discrete equations. Using Anselone' and Stepleman' asymptotically compact theory theorem, the existence, the unicity , the convergence and the error estimate with O(h^3) of the discrete equations are shown. By fixed-point arguments of Ostrowski, a modified Newton iteration with the third order is presented. Numerical examples show that their methods are effective.

关 键 词：求积法 非线性边值问题 边界积分方程 

分 类 号：O241.82[理学—计算数学]