Numerical computational method in solving Fredholm integral equations of the second kind by using Coifman wavelet

RETRACTED ARTICLE: Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

“…Since 1991 the various types of wavelet methods have been applied for the numerical solution of different kinds of integral equations [3]. Namely, the Haar wavelets method [3], Legendre wavelets method [4], Rationalized haar wavelet [5], Hermite cubic splines [6], Coifman wavelet scaling functions [7], CAS wavelets [8], Bernoulli wavelets [9], wavelet preconditioned techniques [25][26][27][28]. Some of the papers are found for solving Abel s integral equations using the wavelet based methods, such as Legendre wavelets [10] and Chebyshev wavelets [11].…”

Low memory requirement and computational time method for solving a class of integral equations

“…Consider the second-kind linear Fredholm integral equation of the form the f (x) and K(x, t) are known functions and y(x) is the unknown function that is to be determined. This type of equations has been solved in many papers with many different methods [1][2][3][4][5][6]. Wavelet bases have been used recently which, primarily because of their local supports and vanishing moment properties, lead to a sparse matrix.…”

A new class of fredholm integral equations of the second kind with non symmetric kernel: solving by wavelets method

“…Integral equation perform role effectively in many fields of science and engineering. Recently, there are a lot of orthonormal basis function that have been used to find an approximate solution, mention Fourier functions [2], Legendre polynomials [21] and wavelets [10,12,13,16,17,19,20,26]. Although, the wavelet bases are one of the most interesting basis, especially for large scale problems, in which the kernel can be constituted as sparse matrix.…”

“…For instance, collocation methods are studied in [15,24], spectral methods are given in [14,18], transform methods are introduced in [1,3,23], and homotopy perturbation method is presented in [8] and others. More recently, the multiresolution analysis has been considered by many researchers (see [11,12,17,19,20,28]). We mention that wavelets method play a key role to find the unique solution for some Fredholm integral equations.…”