Numerical integration rules based on B-spline bases

TL;DR

This paper introduces new numerical integration formulas based on B-spline relations, extending the trapezoidal rule to higher orders and multiple dimensions, supported by theoretical proofs and numerical experiments.

Contribution

It presents novel integration rules derived from B-spline relations, achieving arbitrary order accuracy and extending to multiple dimensions.

Findings

New integration formulas with proven order of accuracy

Extension of rules to multi-dimensional integration

Numerical experiments confirming theoretical results

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 [1]. 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.