Projection and Iterated Projection Methods for Nonlinear Integral equations

DOI10.1137/0724087zbMath0655.65146OpenAlexW1978142553MaRDI QIDQ3802572

Florian A. Potra, Kendall E. Atkinson

Publication date: 1987

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/6bbce6ae702b9a26f73c0b171c900c1c45383ad3

zbMATH Keywords

collocation methodGalerkin methodnumerical examplesHilbert spacesuperconvergenceBanach spaceUrysohn integral equationsisolated fixed pointcompletely continuous mappingiterated projection method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (85)

Superconvergence of the iterated degenerate kernel method ⋮ Wilson wavelets-based approximation method for solving nonlinear Fredholm–Hammerstein integral equations ⋮ Fast multilevel augmentation method for nonlinear integral equations ⋮ Projection Methods for Neural Field Equations ⋮ SPECTRAL APPROXIMATION METHODS FOR FREDHOLM INTEGRAL EQUATIONS WITH NON-SMOOTH KERNELS ⋮ A Note on Asymptotic Expansions to Approximate Eigenvalues of Integral Operators with Green's Kernels using the Iterated Galerkin Method ⋮ Triangular functions for numerical solution of the nonlinear Volterra integral equations ⋮ Superconvergence of the iterated collocation methods for Hammerstein equations ⋮ The numerical solution of Fredholm-Hammerstein integral equations by combining the collocation method and radial basis functions ⋮ Convergence analysis of discrete Legendre spectral projection methods for Hammerstein integral equations of mixed type ⋮ Fast Fourier-Galerkin methods for nonlinear boundary integral equations ⋮ Numerical analysis of a collocation method for functional integral equations ⋮ New numerical process solving nonlinear infinite-dimensional equations ⋮ Positive and nontrivial solutions for the Urysohn integral equation ⋮ Richardson extrapolation for the iterated Galerkin solution of Urysohn integral equations with Green's kernels ⋮ A sinc quadrature method for the Urysohn integral equation ⋮ Error analysis of reiterated projection methods for Hammerstein integral equations ⋮ The numerical solution of nonlinear integral equations of the second kind using thin plate spline discrete collocation method ⋮ Multilevel augmentation methods for solving the sine-Gordon equation ⋮ Unnamed Item ⋮ Spectral approximation methods for nonlinear integral equations with non-smooth kernels ⋮ Modified projection method for Urysohn integral equations with non-smooth kernels ⋮ Discrete Galerkin and iterated discrete Galerkin methods for derivative-dependent Fredholm-Hammerstein integral equations with Green's kernel ⋮ Discrete modified projection method for Urysohn integral equations with smooth kernels ⋮ Superconvergent multi-Galerkin method for nonlinear Fredholm-Hammerstein integral equations ⋮ New approach to solve two-dimensional Fredholm integral equations ⋮ Spline quasi-interpolating projectors for the solution of nonlinear integral equations ⋮ On the numerical solution of a population growth model of a species living in a closed system based on the moving least squares scheme ⋮ Existence, uniqueness, and numerical approximation of solutions of a nonlinear functional integral equation ⋮ A computational approach for solving third kind VIEs by collocation method based on radial basis functions ⋮ Multilevel augmentation methods for nonlinear boundary integral equations II: Accelerated quadratures and Newton iterations ⋮ About a numerical method of successive interpolations for functional Hammerstein integral equations ⋮ Spectral Methods For Hammerstein Integral Equations with Nonsmooth Kernels ⋮ A fast multiscale solver for modified Hammerstein equations ⋮ Modified projection and the iterated modified projection methods for nonlinear integral equations ⋮ Unnamed Item ⋮ The numerical method of successive interpolations for Fredholm functional integral equations ⋮ A meshless method based on the moving least squares (MLS) approximation for the numerical solution of two-dimensional nonlinear integral equations of the second kind on non-rectangular domains ⋮ Iterated discretization ⋮ Application of sinc-collocation method for solving a class of nonlinear Fredholm integral equations ⋮ Superconvergence of Iterated Galerkin Method for a Class of Nonlinear Fredholm Integral Equations ⋮ A novel and efficient numerical algorithm for solving 2D Fredholm integral equations ⋮ On implicitly linear and iterated collocation methods for Hammerstein integral equations ⋮ A modified iterated projection method adapted to a nonlinear integral equation ⋮ A survey of numerical methods for solving nonlinear integral equations ⋮ Convergence analysis of Legendre spectral projection methods for Hammerstein integral equations of mixed type ⋮ Discrete Legendre spectral Galerkin method for Urysohn integral equations ⋮ Error analysis of polynomial-based multi-projection methods for a class of nonlinear Fredholm integral equations ⋮ Spline approximation for second order fredholm integro-differential equations ⋮ Approximation methods for system of linear Fredholm integral equations of second kind ⋮ Superconvergent methods based on quasi-interpolating operators for Fredholm integral equations of the second kind. ⋮ Superconvergent Nyström method for Urysohn integral equations ⋮ Superconvergent Nyström and degenerate kernel methods for Hammerstein integral equations ⋮ Legendre spectral projection methods for Urysohn integral equations ⋮ Superconvergent product integration method for Hammerstein integral equations ⋮ The discrete collocation method for Fredholm–Hammerstein integral equations based on moving least squares method ⋮ Fast multilevel augmentation methods for nonlinear boundary value problems ⋮ Asymptotic error analysis of a quadrature method for integral equations with Green's function kernels ⋮ Solving the nonlinear Poisson equation on the unit disk ⋮ Orthogonal polynomials for the solution of semi linear two-point boundary value problems ⋮ On the numerical solution of some semilinear elliptic problems. II ⋮ Superconvergence of interpolated collocation solutions for Hammerstein equations ⋮ Numerical solution of Urysohn integral equations using the iterated collocation method ⋮ Superconvergence results for the nonlinear Fredholm-Hammerstein integral equations of second kind ⋮ Approximation methods for system of nonlinear Fredholm-Hammerstein integral equations ⋮ Approximating the solution of three-dimensional nonlinear Fredholm integral equations ⋮ A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method ⋮ An approximate solution of bivariate nonlinear Fredholm integral equations using hybrid block-pulse functions with Chebyshev polynomials ⋮ Multilevel methods for the approximation of singular solutions of completely continuous operator equations ⋮ Approximate solution of Urysohn integral equations with non-smooth kernels ⋮ Convergence analysis for derivative dependent Fredholm-Hammerstein integral equations with Green's kernel ⋮ Sinc Projection Solutions of Fredholm Integral Equations ⋮ Convergence analysis of a highly accurate Nyström scheme for Fredholm integral equations ⋮ Richardson Extrapolation of Superconvergent Projection-Type Methods for Hammerstein Equations* ⋮ A discrete collocation scheme to solve Fredholm integral equations of the second kind in high dimensions using radial kernels ⋮ Unnamed Item ⋮ New methods for solving of nonlinear weakly singular integral equations ⋮ The discrete collocation method for weakly singular Urysohn equations ⋮ Numerical methods based on spline quasi-interpolating operators for Hammerstein integral equations ⋮ Application of radial basis function method for solving nonlinear integral equations ⋮ DISCRETE MODIFIED PROJECTION METHODS FOR URYSOHN INTEGRAL EQUATIONS WITH GREEN’S FUNCTION TYPE KERNELS ⋮ Projection methods for approximate solution of a class of nonlinear Fredholm integro-differential equations ⋮ Asymptotic error expansion of the iterated superconvergent Nyström method for Urysohn integral equations ⋮ Some recent numerical methods for solving nonlinear Hammerstein integral equations ⋮ A superconvergent projection method for nonlinear compact operator equations

This page was built for publication: Projection and Iterated Projection Methods for Nonlinear Integral equations