A fast multiscale solver for modified Hammerstein equations

DOI10.1016/j.amc.2011.08.022zbMath1250.65156OpenAlexW2045695039MaRDI QIDQ426295

Yongdong Zhang, Jianfei Li, Zhongying Chen

Publication date: 11 June 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.08.022

zbMATH Keywords

algorithmcomputational complexitynumerical examplesnonlinear integral equationsmultiscale methodsoptimal error estimatefast solversmultilevel augmentation methodsHammerstein equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Systems of nonlinear integral equations (45G15)

Related Items

Discrete Legendre spectral methods for Hammerstein type weakly singular nonlinear Fredholm integral equations ⋮ Legendre spectral projection methods for Fredholm-Hammerstein integral equations ⋮ Multilevel augmentation methods with matrix compression for solving reformulated Hammerstein equations ⋮ Superconvergence results of Legendre spectral projection methods for weakly singular Fredholm-Hammerstein integral equations ⋮ Superconvergence Results for Weakly Singular Fredholm–Hammerstein Integral Equations ⋮ Superconvergence of Legendre spectral projection methods for Fredholm-Hammerstein integral equations ⋮ Superconvergence results for the nonlinear Fredholm-Hammerstein integral equations of second kind ⋮ Approximation methods for system of nonlinear Fredholm-Hammerstein integral equations ⋮ Convergence analysis for derivative dependent Fredholm-Hammerstein integral equations with Green's kernel ⋮ Legendre spectral Galerkin and multi-Galerkin methods for nonlinear Volterra integral equations of Hammerstein type

Cites Work

• Unnamed Item
• Unnamed Item
• Existence of solutions to nonlinear Hammerstein integral equations and applications
• Regularity of the solution of Hammerstein equations with weakly singular kernel
• A survey of numerical methods for solving nonlinear integral equations
• Numerical solutions for weakly singular Hammerstein equations and their superconvergence
• Using the matrix refinement equation for the construction of wavelets on invariant sets
• Superconvergence of the iterated collocation methods for Hammerstein equations
• The Petrov-Galerkin method for second kind integral equations. II: Multiwavelet schemes
• Wavelet Galerkin methods for second-kind integral equations
• Nonlinear functionals of wavelet expansions -- adaptive reconstruction and fast evaluation
• Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
• Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
• Extrapolation of a discrete collocation-type method of Hammerstein equations
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• Extrapolation of Nyström solution for two-dimensional nonlinear Fredholm integral equations
• Fast numerical collocation solutions of integral equations
• Fast wavelet transforms and numerical algorithms I
• A multilevel augmentation method for solving ill-posed operator equations
• Degenerate Kernel Method for Hammerstein Equations
• Fast Multilevel Augmentation Methods for Solving Hammerstein Equations
• Superconvergence of a Collocation-type Method for Hummerstein Equations
• A Discrete Collocation-Type Method for Hammerstein Equations
• Superconvergence of a Collocation-Type Method for Simple Turning Points of Hammerstein Equations
• Projection and Iterated Projection Methods for Nonlinear Integral equations
• A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
• A construction of interpolating wavelets on invariant sets
• Approximate Solutions of Operator Equations
• The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations
• Fast Collocation Methods for Second Kind Integral Equations
• A New Collocation-Type Method for Hammerstein Integral Equations
• Superconvergence of the Iterated Galerkin Methods for Hammerstein Equations
• Theoretical Numerical Analysis
• Galerkin's perturbation method and the general theory of approximate methods for non-linear equations
• Extrapolation of Nyström solution for two dimensional nonlinear Fredholm integral equations
• A multilevel method for solving operator equations
• Discrete wavelet Petrov--Galerkin methods