Solution of the convolution type Volterra integral equations of the first kind by the quadrature-sum method

Some algorithm is presented for solving the convolution type Volterra integral equation of the first kind by the quadrature-sum method. We assume that the integral equation of the first kind cannot be reduced to an integral equation of the second kind but we do not assume that either the kernel or some of its derivatives at zero are unequal to zero. For the relations we propose there is given an estimate of the error of the calculated solution. Some examples of numerical experiments are presented to demonstrate the efficiency of the algorithm.