Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods |
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Authors: | Pan Cheng Jin Huang |
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Affiliation: | (1) Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 804011887, USA;(2) Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, 1678 Nicosia, Cyprus |
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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 −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. |
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