The optimal quadratures for numerical solving of integral Volterra equations and the Cauchy problem

The equations for optimal subgrid points and quadrature coefficients in the problems of numerical solution of integral Volterra equations and the Cauchy problem are obtained. The optimality is regarded as the minimum of the sum of squares of approximation errors in all subgrid points under condition that the last subgrid point is equal to the right end of the subgrid. The optimal points are numerically found for various numbers of subgrid points.