Author(s)

Aurelien Goudjo¹, Louis Kouye²

¹Faculty of Science and Technic (FAST), Abomey-Calavi University (UAC) Abomey-Calavi, Benin, West Africa.
²Institute of Mathematics and Physics Sciences (IMSP), Abomey-Calavi University (UAC), Porto-Novo, Benin, West Africa.

Newton’s method is used to find the roots of a system of equations f (x) = 0. It is one of the most important procedures in numerical analysis, and its applicability extends to differential equations and integral equations. Analysis of the method shows a quadratic convergence under certain assumptions. For several years, researchers have improved the method by proposing modified Newton methods with salutary efforts. A modification of the Newton’s method was proposed by McDougall and Wotherspoon [1] with an order of convergence of 1+ √2. On a new type of methods with cubic convergence was proposed by H. H. H. Homeier [2]. In this article, we present a new modification of Newton method based on secant method. Analysis of convergence shows that the new method is cubically convergent. Our method requires an evaluation of the function and one of its derivatives.

Newton’s Methods, Secant Method, Cubic Convergence, Iterative Method

Goudjo, A. and Kouye, L. (2021) A New Modification of Newton Method with Cubic Convergence. Advances in Pure Mathematics, 11, 1-11. doi: 10.4236/apm.2021.111001.