INFORMATION AND COMPUTATION TECHNOLOGIES

On approximation of definite integrals by compound quadrature formulas using derivatives

V. V. Shustov

State Research Institute of Aviation Systems

Abstract: The problem of computing a definite integral of a function for which the values of itself and the set of derivatives up to a given order at the points of the interval of integration are known is considered. Composite quadrature formulas are constructed that use the values of the function and its derivatives up to the m-th order inclusive. A representation of the remainder is obtained, expressed in terms of the derivative of the corresponding order and the number of nodal points. Examples of integration of the given functions with the study of the error and its estimation are given. A comparison is made with the known numerical methods and the Euler-Maclaurin formula, which showed increased accuracy and better convergence of the two-point integration method.

Keywords: quadrature formulas using derivatives, compound quadrature formula, remainder of integration, approximation error estimate, Euler-Maclaurin formula.

UDC: 519.644

MSC: 41A55

DOI: 10.26117/2079-6641-2021-34-1-88-104