Aims to present a boundary integral equation method for solving Laplace's equation Δu=0 with nonlinear boundary conditions.
The nonlinear boundary value problem is reformulated as a nonlinear boundary integral equation, with u on the boundary as the solution being sought. The integral equation is solved numerically by using the collocation method on smooth or nonsmooth boundary; the singularities of solution degrade the rates of convergence.
Variants of the methods for finding numerical solutions are suggested. So these methods have been compared with respect to number of iterations.
Numerical experiments show the efficiency of the proposed methods.
Provides new methods to solve nonlinear weakly singular integral equations and discusses difficulties that arise in particular cases.
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