Numerical integration rules based on B-spline bases

Abstract

In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in amat et al. (2022). The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove the order of approximation and extend the results to several dimensions. Finally, some numerical experiments are performed in order to check the theoretical results.