# Mechanical quadrature methods and extrapolation for solving nonlinear boundary H

Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations

Abstract：This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations.The methods have high accuracy of order O(h3) 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 h3-Richardson extrapolation algorithms (EAs),the accuracy to the order of O(h5) 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.

Author：

Pan CHENG[1] Jin HUANG[2] Zhu WANG[3]

School of Science, Chongqing Jiaotong University, Chongqing 400074, P. R. ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China,Chengdu 611731, P. R. ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China,Chengdu 611731, P. R. China;Department of Mathematics, Virginia Polytechnic Institute and State University,Blacksburg, VA 24061, USA

Journal：

Applied Mathematics and Mechanics

2011, 32(12)

O24 O39

Keywords：

Helmholtz equation

Newton iteration

nonlinear boundary condition

O1 O24

integral equations Helmholtz nonlinear boundary nonlinear system stability and convergence algorithms Newton iteration high accuracy fixed point order presents theory simple paper based EAs

the National Natural Science Foundation of China，the Natural Science Foundation Project of Chongqing，the Air Force Office of Scientific Research，the National Science Foundation

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