Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations |
| |
Authors: | Pan Cheng Jin Huang Zhu Wang |
| |
Institution: | Pan CHENG 1,Jin HUANG 2,Zhu WANG 2,3 (1. School of Science,Chongqing Jiaotong University,Chongqing 400074,P. R. China,2. School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,3. Department of Mathematics,Virginia Polytechnic Institute and State University,Blacksburg,VA 24061,USA) |
| |
Abstract: | 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. |
| |
Keywords: | Helmholtz equation mechanical quadrature method Newton iteration nonlinear boundary condition |
本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录! |
|