Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications

Obadah Said Solaiman, Ishak Hashim

Research output: Contribution to journalArticle

Abstract

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?

Original languageEnglish
Article number1728965
JournalMathematical Problems in Engineering
Volume2019
DOIs
Publication statusPublished - 1 Jan 2019

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Chemical engineering
Engineering Application
Nonlinear equations
Efficacy
Nonlinear Equations
Chemical reactors
Predictor-corrector
Newton-Raphson method
Halley's Method
Efficiency Index
Derivatives
Chemical Reactors
Van Der Waals
Equilibrium Problem
Second derivative
Convergence Analysis
Newton Methods
High Efficiency
Binary
Demonstrate

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications. / Said Solaiman, Obadah; Hashim, Ishak.

In: Mathematical Problems in Engineering, Vol. 2019, 1728965, 01.01.2019.

Research output: Contribution to journalArticle

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