Secant Method Superiority Over Newton’s Method in Solving Scalar Nonlinear Equations

Abstract

This study is aimed to pinpoint the cases or situations that makes the performance of secant method superior than the performance of New- ton’s method in solving certain selected nonlinear equations. Despite the convergence order of Newton’s method that is higher, that does not necessarily mean it performs faster than secant method for all nonlinear problems. In addition, both methods are almost identical in their approach and secant method has advantages that can make its performances superior or equivalent to Newton’s method for some nonlinear equations. Four numerical experiments are given to clarify the situations in which the performance of secant method are proven to be superior over Newton’s method.