Some variants of Halley’s method with memory and their applications for solving several chemical problems

Abstract

In this paper, we develop some variants of the well-known Halley’s iterative method to solve nonlinear equations. The resulting methods are one-step methods, with and without memory, which use different number of functional evaluations per iteration. Those with memory have higher efficiency indexes than Newton’s scheme and also than many known optimal iterative procedures without memory. Their dependence on the initial estimation is studied by using real multidimensional dynamical techniques, showing their stable behavior. This is also checked with some numerical examples, that illustrate the performance of the proposed methods compared with other well-known schemes in the literature. For all the examples considered, that include chemical equilibrium problems, global reaction rates in packed bed reactors or continuous stirred tank reactors, the methods with memory reach the approximations to the roots, within the established tolerance, using fewer number of functional evaluations than their partners.