On Convergence of Different Quadrature Rules of Numerical Integration and Error Estimations

Abstract

In this present manuscript the error occurred in different standard quadrature rules of numerical integrations using set of numerical data of the function  corresponding to equidistant values of argument  have been studied. With the different form of functions  numerical outputs have been obtained for the definite integral in certain limits with different sub intervals of the range of integral to compare the error estimation, rate of convergence of particular rule of integration and accuracy of the outcomes. The standard rules of numerical integration known as Trapezoidal, Simpson’s one­ third, Simpson’s three eighth rules including Newton-Cotes formula has been discussed. It has been concluded that the Simpson’s one-third rule of integration is more effective and accurate after graphical and numerical comparison.