Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov–Galerkin method

Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets

“…One possibility for it is to make use of the Haar wavelets, which are mathematically the most simple wavelets. Also, many different basis functions have been used to solve and reduce integral equations to a system of algebraic equations [1][2][3][4][5][6][7][8][9][10][11][12]. The aim of this work is to present a numerical method for approximating the solution of nonlinear Fredholm integral equation of the second kind:…”

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

“…The collocation techniques are involved in . For the numerical solution of Fredholm integral equations, Galerkin methods are used in . Other methods use spline functions and wavelets , product integration , homotopy analysis techniques homotopy perturbation and Adomian decomposition method , polynomial interpolation procedures and suboptimal trajectories , multigrid methods .…”

Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind

“…Volterra integral equations find application in demography, the study of viscoelastic materials, and in insurance mathematics through the renewal equation. Fredholm equations [4] arise naturally in the theory of signal processing, most notably as the famous spectral concentration problem popularized by David Slepian [4]. They also commonly arise in linear forward modeling and inverse problems.…”