IJSRST151420 | Received: 09 October 2015 | Accepted: 16 October 2015 | September-October 2015 [(1)4: 80-83] © 2015 IJSRST | Volume 1 | Issue 4 | Print ISSN: 2395-6011 | Online ISSN: 2395-602X Themed Section: Science and Technology 80 A Simple Hybrid Method for Finding the Root of Nonlinear Equations Hassan Mohammad Department of Mathematical Sciences, Faculty of Sciences, Bayero University, Kano, Kano State, Nigeria ABSTRACT In this paper, we proposed a simple modification of McDougall and Wotherspoon [11] method for approximating the root of univariate function. Our modification is based on the approximating the derivative in the corrector step of the proposed McDougall and Wotherspoon Newton like method using secant method. Numerical examples demonstrate the efficiency of the proposed method. Keywords: Secant method, Predictor- corrector, Nonlinear equations Mathematics Subject Classification: 65K05, 65H05, 65D32, 34G20 I. INTRODUCTION Consider a problem for solving nonlinear equation of the form where f : R → R is continuously differentiable function suppose there is a solution x ∗ ∈ R for which f (x ∗ ) = 0. Newton’s method is one of the famous and well known method of solving equation (1)[11] Newton’s method iteratively produces a sequence{x k } of approximations that converges quadratically to a simple root x∗ from any given initial point x 0 ∈ R, in the neighborhood of x ∗ via: In an attempt to reduce the computational cost of Newton’s method, secant methods have been introduced [5]. These methods approximate the derivative in Newton’s method using secant line. Starting with two estimate of the root x−1, x 0 .the iterate formula is given by The convergence rate of secant method is normally superlinear. Several modifications of Newton method was given in order to reduce its computational cost or to increase its rate of convergence, see, for example, [2, 6, 8, 10, 13, 14] and reference therein. For determining the root of a nonlinear equation, Weerakoon and Fernando [16], suggest an improvement to the iteration of Newton’s method which involves an definite integral of the derivative of the function, and the relevant area is approximated by rectangular rule. Homeier [3], consider a modification of Newton method for finding zero of a univariate function. The modification converges cubically. Per iteration it requires one evaluation of the function and two evaluation of its derivative. Thus, the modification is suitable if the calculation of the derivative has a similar or lower cost than that of the function itself. Ozban [12], present some new variants of Newton method based on harmonic mean and midpoint integration rule. The order of convergence of the proposed method is three. Kou et al. [7], present a new modification of Newton’s method for solving nonlinear equation which converges cubically. The modification requires two function evaluation and one first derivative evaluation. Thus, the new method is preferable if the computational cost of the first derivative is equal or more than those of the function itself. Jayakumar [5], presents a new class of Newton’s method for solving single nonlinear equation. The method is the generalization of Simpson’s integral rule applied on the Newton’s theorem.