Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods

Authors:
Pan Cheng;Jin Huang
Affiliations:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China 611731 and School of Science, Chongqing Jiaotong University, Chongqin ...;School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China 611731
Venue:
Numerical Algorithms
Year:
2011

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Abstract

We study the numerical solution procedure for two-dimensional Laplace's equation subjecting to non-linear boundary conditions. Based on the potential theory, the problem can be converted into a nonlinear boundary integral equations. Mechanical quadrature methods are presented for solving the equations, which possess high accuracy order O(h 3) and low computing complexities. Moreover, the algorithms of the mechanical quadrature methods are simple without any integration computation. Harnessing the asymptotical compact theory and Stepleman theorem, an asymptotic expansion of the errors with odd powers is shown. Based on the asymptotic expansion, the h 3驴驴Richardson extrapolation algorithms are used and the accuracy order is improved to O(h 5). The efficiency of the algorithms is illustrated by numerical examples.