Chebyshev spectral-collocation method for Volterra integral equations

A Chebysheve spectral-collocation method is proposed to solve the Volterra integral equations of the second kind. The biggest advantage for the proposed method is that only the Chebyshev Gauss points and Chebyshev weights, which can be obtained easily and accurately, are used in this method. This enables us to avoid the complex computation of the Legendre Gauss points and the Legendre weights. Numerical examples are presented to show that the numerical errors decay in exponential rate. Our next work is the convergence analysis for the proposed method, which is in progress.