SOLVING DEFINITE INTEGRALS USING NUMERICAL METHOD
Keywords:
Keywords. Sobolev space, optimal error function, Lagrange multipliers, Wandermonde determinant, derivative optimal quadrature formula.Abstract
Abstract. In this work, an algorithm for constructing the effective formula for numerical computation of definite integrals in space is given. Using this algorithm, a derivative quadrature formula is constructed using the first and second order derivatives of the function for equally distributed nodal points on the section [0,1]. For this, the form of the norm of the optimal error functional is found. Finding the conditional extremum of the function was used to minimize the norm of the error function. A system of linear algebraic equations for optimal coefficients is obtained. It is proved that the solution of the system of equations exists and is unique using the Wandermonde determinant. The formula constructed in this work gives good results if the values of the derivatives of the function at the nodes are given.
