The optimal quadratures for numerical solving integral Volterra equations and the Cauchy problem (Q2729360)

The author deals with the problem of an optimal choice of the parameters for quadrature methods which solve Volterra integral equations and Cauchy problems for ordinary differential equations. The optimality means minimality of the sum of squares of the approximation errors in all subgrid points under the condition that the last subgrid point coincides with the right boundary of the subgrid under consideration.NEWLINENEWLINENEWLINEThe author obtains equations for optimal subgrid points and quadrature coefficients. The optimal points are found numerically for various numbers of subgrids points. Analyzing the behavior of the found nodes, the author concludes from the results of numerical experiments that, for the characteristic polynomials corresponding to given nodes, the separability condition of zeros holds.