Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations
type: Item
instance of: scholarly article
title: Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations
zbMATH Open document ID: 1238.35016
author: Pan Cheng
author: Jin Huang
author: Zhu Wang
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2012-03-13T00:00:00Z
review text: The mechanical quadrature method for solving the Helmholtz equation with nonlinear boundary conditions is presented. The advantage of this method is its high accuracy (of order \(\mathcal{O}(h^3)\)), its low computational complexity and the fact that no singular integration is needed. The authors prove stability and convergence for the resulting nonlinear system using the Stepleman theorem. The nonlinear system is solved with the Newton method, and the theory is based on the Ostrowski fixed point theorem. In addition, the accuracy is improved to \(\mathcal{O}(h^5)\) using the \(h^3\)-Richardson extrapolation algorithm. Two numerical examples are presented which are in agreement with the theoretical results.
reviewed by: Andreas Kleefeld
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 6014569
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: integral equations
zbMATH Keywords: mechanical quadrature method
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: Stepleman theorem
zbMATH Keywords: Ostrowski fixed point theorem
zbMATH Keywords: Newton method
MaRDI profile type: Publication
full work available at URL: s10483-011-1519-7
OpenAlex ID: W2334151936
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DOI: 10.1007/S10483-011-1519-7
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description: scientific article; zbMATH DE number 6014569