Mechanical quadrature methods and extrapolation for solving nonlinear problems in elasticity
type: Item
instance of: scholarly article
title: Mechanical quadrature methods and extrapolation for solving nonlinear problems in elasticity
zbMATH Open document ID: 1427.74026
DOI: 10.1155/2018/6932164
author: Pan Cheng
author: Ling Zhang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 74S15
zbMATH DE Number: 7019367
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6932164
OpenAlex ID: W2807415903
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description: scientific article; zbMATH DE number 7019367