Projection and iterated projection methods for nonliear integral equations
SIAM Journal on Numerical Analysis
Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
Superconvergence of the iterated Galerkin methods for Hammerstein equations
SIAM Journal on Numerical Analysis
Numerical Solution of Nonlinear Equations
ACM Transactions on Mathematical Software (TOMS)
Summary of Sinc numerical methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Recent developments of the Sinc numerical methods
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets
Journal of Computational and Applied Mathematics
Global convergence of quasi-Newton methods based on adjoint Broyden updates
Applied Numerical Mathematics
A numerical scheme for a class of nonlinear Fredholm integral equations of the second kind
Journal of Computational and Applied Mathematics
Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Solving nonlinear integral equations in the Urysohn form by Newton-Kantorovich-quadrature method
Computers & Mathematics with Applications
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In this paper, the numerical solution of nonlinear Fredholm integral equations of the second kind is considered by two methods. The methods are developed by means of the Sinc approximation with the single exponential (SE) and double exponential (DE) transformations. These numerical methods combine a Sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the methods. So far approximate solutions with polynomial convergence have been reported for this equation. These methods improve conventional results and achieve exponential convergence. Some numerical examples are given to confirm the accuracy and ease of implementation of the methods.