Series expansion method for weakly singular Volterra integral equations

We propose series expansion method to solve VIEs (Volterra integral equations) with smooth given functions, including weakly singular VIEs possessing unsmooth solution. The key step in proposed method is to approximate given functions by their own Chebyshev Gauss–Lobatto interpolation polynomials. Lubich's results play an important role in the proposed method for weakly singular VIEs. Convergence analysis is provided for proposed method. Numerical experiments are carried out to confirm theoretical results.