Spectral methods for Volterra integral equations of the first kind

We propose a spectral Legendre-Collocation approximation for the linear Volterra integral equations (VIEs) of the first kind. Using this method, solving the first kind integral equation reduces to solving a system of algebraic equations and so the problem can be solved directly. One of advantages of this method in comparison with other algorithms is low cost of computing. Numerical results are presented to confirm the capability and accuracy of proposed method.