On the Order of Convergence of the Trapezoidal and Simpson’s Rule for a Certain Class of Non Differentiable Functions

Abstract

It’s well known from numerical integration theory that the classical order of convergence of the trapezoidal rule is two, for Simpson’s rule is four and they are formulated for functions that have second and fourth continuous derivative, respectively. In this work a certain class of functions that do not satisfy the smoothness requirements mentioned above are studied and it’s proved that the order of convergence can be fractional and at most the same as the classical order. Numerical experiments are shown in order to validate theoretical results.