Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
Applied Numerical Mathematics
Hybrid collocation methods for Fredholm integral equations with weakly singular kernels
Applied Numerical Mathematics
Iteration methods for Fredholm integral equations of the second kind
Computers & Mathematics with Applications
A fast numerical method for a natural boundary integral equation for the Helmholtz equation
Journal of Computational and Applied Mathematics
A Fast Collocation Method for Eigen-Problems of Weakly Singular Integral Operators
Journal of Scientific Computing
Numerical methods for Fredholm integral equations with singular right-hand sides
Advances in Computational Mathematics
Fast multilevel augmentation methods for nonlinear boundary value problems
Computers & Mathematics with Applications
Applied Numerical Mathematics
Advances in Computational Mathematics
Wavelet Collocation Method and Multilevel Augmentation Method for Hammerstein Equations
SIAM Journal on Scientific Computing
Fast Multilevel Augmentation Methods for Nonlinear Boundary Integral Equations
SIAM Journal on Numerical Analysis
A fast solver for integral equations with convolution-type Kernel
Advances in Computational Mathematics
Iterated Fast Collocation Methods for Integral Equations of the Second Kind
Journal of Scientific Computing
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In this paper we develop fast collocation methods for integral equations of the second kind with weakly singular kernels. For this purpose, we construct multiscale interpolating functions and collocation functionals having vanishing moments. Moreover, we propose a truncation strategy for the coefficient matrix of the corresponding discrete system which forms a basis for fast algorithms. An optimal order of convergence of the approximate solutions obtained from the fast algorithms is proved and the computational complexity of the algorithms is estimated. The stability of the numerical method and the condition number of the truncated coefficient matrix are analyzed.