High Order Quadrature Based Iterative Method for Approximating the Solution of Nonlinear Equations

In this paper, weight function and composition techniques are utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a twopoint quadrature based method of convergence order ρ = 3 with efficiency index EI = 1.3161 to a three-point method of convergence order ρ = 8 with EI = 1.5157 at the cost of one additional function evaluation. The method is used to approximate the solution of some nonlinear equations and the results generated are compared with that of some existing methods. Numerical results shows that method developed here in is very efficient in approximation of solution of nonlinear equations.