Error Estimation of Numerical Integration Methods

Abstract

We compare the accuracy of numerical integral methods like Newton-Cotes method and Gaussian Quadrature Rule (GQR) for the model problem and tested for another problem to verify the results. From results we notice that error of GQR is about 10 times less than Newton-Cotes formulas. For this reason we prefer GQR over other methods. But GQR uses nodes and weights which is a tedious work. This difficulty can overcome by using the idea of  ”three-term recurrence” relation. We can transform the problem of finding the nodes and weights for GQR to one of finding eigenvalues and eigenvectors of a symmetric tridiagonal matrix.

Keywords: Numerical integration; Gaussian Quadrature rules; error estimate; convergence rate.