Solution of the Convolution Type Volterra Integral Equations of the First Kind by the Quadrature-Sum Method

Abstract: Some algorithm is presented for solving the convolution type Volterra integral equation ofthe first kind by the quadrature-sum method. We assume that the integral equation of the firstkind cannot be reduced to an integral equation of the second kind but we do not assume thateither the kernel or some of its derivatives at zero are unequal to zero. For the relations wepropose there is given an estimate of the error of the calculated solution. Some examples ofnumerical experiments are presented to demonstrate the efficiency of the algorithm. © 2020, Pleiades Publishing, Ltd.