Two-dimensional wavelets for numerical solution of integral equations

Numerical solution of linear Fredholm integral equations via two-dimensional modification of hat functions

“…3 illustrate the error results for this example. Also, we compare the absolute error computed for the selected grid points by the present method and haar wavelets method [28] in Table 4. This fact is obvious from Table 4 that the results obtained by the present method is better than that obtained in [28].…”

“…All computations have been performed on a Intel CPU PC. using a Matlab code.Example 1[28]. Consider the following two-dimensional linear Fredholm integral equation: f ðx; yÞ ¼ x cosðyÞ À sinðtÞ þ 1Þf ðs; tÞdsdt; ðx; yÞ 2 D;…”

A wavelet Galerkin approximation of Fredholm integral eigenvalue problems with bidimensional Haar functions

“…We have extended the work by Phoon et al [8] to a two-dimensional domain, although (nonhomogeneous) Fredholm integral equations have been solved with 2D Haar wavelets elsewhere [4]. Forthcoming work comprises testing additional covariance functions and providing error estimates for the approximate eigenvalues and eigenfunctions.…”

“…In this study, we highlight the Galerkin method with wavelet shape functions [3,4,5,8] for the computation of the eigenpairs of the covariance in the two-dimensional case. To accomplish the task, we use two-dimensional Haar wavelet basis functions [2].…”

Numerical Solution of Two Dimensional Fredholm Integral Equations of the Second Kind by the Barycentric Lagrange Function*

“…In this paper, we pay attention to the two dimensional linear Fredholm integral equations (FIEs) of the second kind ( ) ( ) ( ) ( ) ( ( ) mensional FIEs, such as the radial basis functions method [4], Haar wavelets [5] and integral mean value method [6] [7]. Berrut specializes the barycentric Lagrangian interpolation formula [8], and some other authors present the corresponding numerical stability analyses in the literatures [9] [10] [11].…”