A new Laguerre wavelets-based method for solving Fredholm integral equations with weakly singular logarithmic kernel

Abstract

In this study, a wavelet-based collocation scheme has been introduced for solving the linear and nonlinear Fredholm integral equations as well as the system of linear Fredholm integral equations with weakly singular logarithmic kernel. Initially, Laguerre wavelets have been constructed by dilation and translation of Laguerre polynomials. For the numerical solution of the Fredholm integral equations, all the functions have been approximated with respect to the Laguerre wavelets. Then, the proposed linear and nonlinear Fredholm integral equations reduce to systems of linear and nonlinear algebraic equations by utilizing the function approximations. Furthermore, the error estimation and the convergence analysis of the presented method have been discussed. Moreover, the numerical results of the several experiments have also been presented in both graphical and tabular form to describe the accuracy and efficiency of the approached method, and also, to determine the validity of the presented scheme, the approximate solutions and absolute error values are compared with the results obtained by other existing approaches.