Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods (Q652336)

The author studies the numerical solution for a two dimensional Laplace's equation subject to nonlinear boundary conditions. Based on potential theory, the problem is converted into a nonlinear integral equation. Mechanical quadrature methods are presented for solving the nonlinear boundary integral equation. A nonlinear system is obtained. Then the error is analyzed to obtain an asymptotic expansion and the Richardson extrapolation is used to achieve the accuracy order of \(O(h^5)\). The efficiency of the algorithms is illustrated by numerical examples.