Meshless methods based on infinitely smooth radial kernels have the potential to provide spectrally accurate function approximations with enormous geometric flexibility in any number of dimensions. The highest accuracy can often be obtained when the shape parameter in the basis function is small. But as the shape parameter goes to zero, the standard RBF interpolant matrix becomes severely ill-conditioned. The ill-conditioning can be reduced using alternate bases. One of these alternative bases is the Hilbert–Schmidt SVD basis. The Hilbert– Schmidt SVD method offers a stable mechanism for converting a set of near-flat kernels with scattered centres to a well-conditioned base for exactly the same space. In this paper, we apply the Gaussian Hilbert–Schmidt SVD basis functions method for solving the linear Fredholm integral equations of the second kind. The method estimates the solution by the discrete collocation method based on Gaussian Hilbert–Schmidt SVD basis functions constructed on a set of disordered data. This approach reduces the solution of the problem under study to the solution of a linear system of algebraic equations. Also, the convergence of the proposed approach is analyzed. Lastly, several numerical experiments are presented to test the stability and accuracy of the proposed method
