Solving Fredholm integral equations of the first kind using Muntz wavelets

The Muntz-Legendre polynomials arise by orthogonalizing the Muntz system {x(lambda 1), x(lambda 2), ....} with respect to the weight function w(x) =1 on [0, 1]. In this paper, we introduce Muntz wavelets by using the Muntz-Legendre polynomials on the interval [0, 1]. Using Jacobi polynomials we make the numerical evaluation of Muntz wavelets more stable. Next, this basis in combination with a matrix method is utilized to solve Fredholm integral equations of the first kind, which have many applications in several fields of computational physics. Errors of the proposed method are studied and numerical results are given to demonstrate the spectral accuracy of the method. We will show that the proposed method, in contrast to other wavelet methods, is capable of providing highly accurate results for solutions with fractional powers. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.