The fluctuationlessness approach to the numerical integration of functions with a single variable by integrating Taylor expansion with explicit remainder term

Abstract

In this paper we give the definition of the Fluctuationlessness concept and using this concept we make approximations to univariate functions by using Taylor expansion with the explicit remainder term. Then integrating this approximate expression we obtain a new quadrature-like numerical integration method. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the remainder term and errors are analyzed.