  This paper presents a direct numerical scheme to approximate the solution of
all classes of nonlinear Volterra integral equations of the first kind. This
computational method is based on operational matrices and vectors. The
operational vector for hybrid block pulse functions and Chebyshev polynomials
is constructed. The scheme transforms the integral equation to a matrix
equation and solves it with a careful estimate of the error involved. The main
characteristic of the scheme is the low cost of setting up the equations
without using any projection method which is the consequence of using
operational vectors. Simple structure to implement, low computational cost and
perfect approximate solutions are the major points of the presented method.
  Error analysis and comparisons with other existing schemes demonstrate the
efficiency and the superiority of our scheme.
