【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.更多还原

【Abstract】 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.更多还原