Optimization of the Euler-Maclaurin type quadrature formula in the Hilbert space of periodic functions

This paper proposes a method for solving the problems of the Euler - Bernoulli beam, in which the problem is reduced to the solution of the Fredholm integral equation of the second kind. This integral equation is solved by the method of optimal quadrature formulas with derivatives. Then,using the Green function, the analytic solution is determined. Different boundary conditions can be used to determine the numerical and analytical solutions. results from other researchers to illustrate the performance of the proposed method