Projection and iterated projection methods for nonliear integral equations
SIAM Journal on Numerical Analysis
A discrete collocation-type method for Hammerstein equations
SIAM Journal on Numerical Analysis
Norms of inverses and condition numbers for matrices associated with scattered data
Journal of Approximation Theory
SIAM Journal on Applied Mathematics
An efficient numerical scheme for Burgers' equation
Applied Mathematics and Computation
Applied Mathematics and Computation
On the use of boundary conditions for variational formulations arising in financial mathematics
Applied Mathematics and Computation
Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations
Journal of Computational and Applied Mathematics
Solution of a class of two-dimensional integral equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Radial Basis Functions
Numerical Mathematics (Texts in Applied Mathematics)
Numerical Mathematics (Texts in Applied Mathematics)
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Solving a system of nonlinear integral equations by an RBF network
Computers & Mathematics with Applications
Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
Journal of Computational and Applied Mathematics
A meshless based method for solution of integral equations
Applied Numerical Mathematics
Large-scale methods in image deblurring
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Universal quadratures for boundary integral equations on two-dimensional domains with corners
Journal of Computational Physics
On a method for solving a two-dimensional nonlinear integral equation of the second kind
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this paper, we present a numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on a non-rectangular domain. The method utilizes radial basis functions (RBFs) constructed on scattered points as a basis in the discrete collocation method. The proposed scheme is meshless, since it does not need any domain element and so it is independent of the geometry of the domain. The method reduces the solution of the two-dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations. Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of the new technique.