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In this study, we propose a modified predictor-corrector Newton-Halley (MPCNH) method for solving nonlinear equations. The proposed sixteenth-order MPCNH is free of second derivatives and has a high efficiency index. The convergence analysis of the modified method is discussed. Different problems were tested to demonstrate the applicability of the proposed method. Some are real life problems such as a chemical equilibrium problem (conversion in a chemical reactor), azeotropic point of a binary solution, and volume from van der Waals equation. Several comparisons with other optimal and nonoptimal iterative techniques of equal order are presented to show the efficiency of the modified method and to clarify the question, are the optimal methods always good for solving nonlinear equations?

Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications