Convergence of approximate solution of nonlinear Fredholm–Hammerstein integral equations

An operational approach with Pade approximant for the numerical solution of non-linear Fredholm integro-differential equations

“…Analytically, solving these problems are difficult, so many authors are encouraged to solve these problems numerically. Some of the new important numerical methods are briefly described as follows: Maleknejad et al [1] proposed the cubic semi-orthogonal compactly supported B-spline wavelets as a basis functions for solution of nonlinear Fredholm-Hammerstein integral equations of the second kind. A discretized version of the Adomian decomposition method was introduced and called Discrete Adomian Decomposition Method (DADM) in [2].…”

Convergence analysis for numerical solution of Fredholm integral equation by Sinc approximation

“…Numerical and theoretical methods for solving integro-differential and integral equations have been studied by many authors so far [1][2][3][4][5][6][7][8][9]. Some of them usually use techniques based on an expansion in terms of some basis functions or use some quadrature formulas, and the convergence rate of these methods are usually of polynomial order with respect to N where N represents the number of terms of the expansion or the number of points of the quadrature formula.…”

Semi-Orthogonal Spline Scaling Functions for Solving Hammerstein Integral Equations

“…The cubic semi-orthogonal compactly supported B-spline wavelets has been used in Ref. 24, and proved that the convergence of method is exponentially with rate of O(2 −4j ). The collocation method based on Daubechies wavelets and combined with the standard collocation method has been introduced in Ref.…”