A New Accelerated Third-Order Two-Step Iterative Method for Solving Nonlinear Equations

Abstract

In the paper a new two-step iterative method has been suggested for estimating nonlinear problems by using quadrature formula. We have also proved that the proposed two-step iterative method has third-order of convergence. For the duration of study, it has been detected that the third-order iterative Method faster than existing cubic Methods such as variant of Newton Raphson Method and Halley Method. Numerous numerical illustrations are specified to demonstrate the efficiency and the performance of the new two-step method. Henceforth, the third-order iterative Method has been considered as an imperative enhancement and refinement to find the root of nonlinear equations.

Keyword: Non-linear equations, cubic methods, order of convergence, error and accuracy.