共被期刊论文引用了3次
您的检索式：您选中1篇文献正在查看引证文献汇总
|
|
|
题名
|
作者
|
年代
|
出处
|
被引量
|
| 1 | 机械求积法及其外推算法求解Helmholtz非线性边界积分方程显示文摘当Helmholtz微分方程转化为非线性边界积分方程后,可以利用机械求积法求得近似解,此方法具有较高的收敛精度阶O(h3)和较低的计算复杂度.构造机械求积法时,一个非线性方程系统通过离散非线性积分方程得到.此外,每个矩阵元素的值都不需要计算任何奇异积分.根据渐近紧理论和Stepleman定理,整个系统的稳定性和收敛性得到了证明.利用h3-Richardson外推算法,收敛精度阶可以提高到O(h5).为了求解非线性方程组,利用Ostrowski不动点定理研究了Newton的解的收敛性.几个算例从数值上说明了本算法的有效性. | 程攀 黄晋 王柱 | 2011 | 应用数学和力学2011，32，12： | 1 |
| 2 | An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications显示文摘In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the approximate eigenpair. Besides, we design a type of cascadic adaptive finite element method for the Steklov eigenvalue problem based on the proposed a posteriori error estimator. In this new cascadic adaptive scheme, instead of solving the Steklov eigenvalue problem in each adaptive space directly, we only need to do some smoothing steps for linearized boundary value problems on a series of adaptive spaces and solve some Steklov eigenvalue problems on a low dimensional space. Furthermore, the proposed a posteriori error estimator provides the way to refine meshes and control the number of smoothing steps for the cascadic adaptive method. Some numerical examples are presented to validate the efficiency of the algorithm in this paper. | Fei Xu Qiumei Huang | 2021 | Science China Mathematics2021，64，3： | 0 |
| 3 | Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations显示文摘This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h 3 ) and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h 3 -Richardson extrapolation algorithms (EAs), the accuracy to the order of O(h 5 ) is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples. | 程攀 黄晋 王柱 | 2011 | Applied Mathematics and Mechanics(English Edition)2011，32，12： | 0 |
您所在的机构暂未开通此部分的功能，请联系管理员