Some weighted quadrature methods based upon the mean value theorems

Abstract

In this paper, a class of weighted quadrature methods is introduced for smooth functions based upon the use of the mean value theorems. These new quadrature rules are also treated in a systematic approach involving formal series expansion. The convergence analysis of the proposed method is studied here for both the non-weighted and the weighted cases. Some potential areas and directions for extensions and applications of the results, which are presented in this paper, are also indicated.