A class of iterative methods with third-order convergence to solve nonlinear equations

Citations of this article
Mendeley users who have this article in their library.


Algebraic and differential equations generally co-build mathematical models. Either lack or intractability of their analytical solution often forces workers to resort to an iterative method and face the likely challenges of slow convergence, non-convergence or even divergence. This manuscript presents a novel class of third-order iterative techniques in the form of xk + 1 = gu (xk) = xk + f (xk) u (xk) to solve a nonlinear equation f with the aid of a weight function u. The class currently contains an invert-and-average(gKia), an average-and-invert(gKai), and an invert-and-exponentiate(gKe) branch. Each branch has several members some of which embed second-order Newton's (gN), third-order Chebychev's (gC) or Halley's (gH) solvers. Class members surpassed stand-alone applications of these three well-known methods. Other methods are also permitted as auxiliaries provided they are at least of second order. Asymptotic convergence constants are calculated. Assignment of class parameters to non-members carries them to a common basis for comparison. This research also generated a one-step "solver" that is usable for post-priori analysis, trouble shooting, and comparison. © 2007 Elsevier B.V. All rights reserved.




Koçak, M. Ç. (2008). A class of iterative methods with third-order convergence to solve nonlinear equations. Journal of Computational and Applied Mathematics, 218(2), 290–306. https://doi.org/10.1016/j.cam.2007.02.001

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free