Projection and iterated projection methods for nonliear integral equations
SIAM Journal on Numerical Analysis
On the boundary element method for some nonlinear boundary value problems
Numerische Mathematik
Projection methods for a class of Hammerstein equations
SIAM Journal on Numerical Analysis
Extrapolation of a discrete collocation-type method of Hammerstein equations
Journal of Computational and Applied Mathematics
Superconvergence of the iterated Galerkin methods for Hammerstein equations
SIAM Journal on Numerical Analysis
Superconvergence of the iterated collocation methods for Hammerstein equations
Journal of Computational and Applied Mathematics
A construction of interpolating wavelets on invariant sets
Mathematics of Computation
Extrapolation of Nystrom Solution for Two-Dimensional Nonlinear Fredholm Integral Equations
Journal of Scientific Computing
Fast Collocation Methods for Second Kind Integral Equations
SIAM Journal on Numerical Analysis
Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
Applied Numerical Mathematics
A Fast Fourier-Galerkin Method for Solving Singular Boundary Integral Equations
SIAM Journal on Numerical Analysis
Fast Multilevel Augmentation Methods for Solving Hammerstein Equations
SIAM Journal on Numerical Analysis
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We propose a fast algorithm for the solution of the nonlinear boundary integral equation resulting from a reformulation of a boundary value problem of the Laplace equation with nonlinear boundary conditions. The fast algorithm is developed by using the multilevel augmentation method (introduced recently by Chen, Wu, and Xu for general nonlinear integral equations), in conjunction with a matrix truncation strategy, and an error control technique of numerical integrations for integrals appeared in the process of solving the equation. We prove that the proposed algorithm has an optimal convergence order (up to a logarithmic factor) and a nearly linear computational complexity order (measured in the number of multiplications and functional evaluations). Numerical experiments are presented to demonstrate its approximation accuracy and computational efficiency, verifying the theoretical estimates, and to compare performance of the proposed algorithm with that of the Atkinson and Chandler algorithm.