Newton Cotes Quadrature R-I Model for the Numerical Simulation of Nonlinear Equations

An innovative set of closed Newton-Cotes quadrature techniques for numerical integration is introduced, using the value of arithmetic mean derivative at the midpoint. The existing closed Newton cotes quadrature technique and the computation of numerical integration using arithmetic mean derivative-based closed Newton cotes quadrature techniques are compared. Additionally, it is demonstrated that the proposed quadrature rule provided more precise solutions and an increase the order of precision (accuracy) over traditional closed Newton-Cotes quadrature formula. Error terms for the proposed approach and the existing approach are compared. Lastly, a few numerical examples show that the suggested approach's numerical superiority over an existing closed Newton-Cotes quadrature formula.