Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications

Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications

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 we...

Full description

Bibliographic Details
Main Authors: Obadah Said Solaiman, Ishak Hashim
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/1728965
id doaj-e21e865fc9964fbba3a14147385d46f3
record_format Article
spelling doaj-e21e865fc9964fbba3a14147385d46f32020-11-25T00:55:19ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/17289651728965Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering ApplicationsObadah Said Solaiman0Ishak Hashim1Preparatory Year Deanship, King Faisal University, 31982 Hofuf, Al-Ahsa, Saudi ArabiaCenter for Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaIn 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?http://dx.doi.org/10.1155/2019/1728965
collection DOAJ
language English
format Article
sources DOAJ
author Obadah Said Solaiman
Ishak Hashim
spellingShingle Obadah Said Solaiman
Ishak Hashim
Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications
Mathematical Problems in Engineering
author_facet Obadah Said Solaiman
Ishak Hashim
author_sort Obadah Said Solaiman
title Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications
title_short Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications
title_full Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications
title_fullStr Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications
title_full_unstemmed Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications
title_sort efficacy of optimal methods for nonlinear equations with chemical engineering applications
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description 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?
url http://dx.doi.org/10.1155/2019/1728965
work_keys_str_mv AT obadahsaidsolaiman efficacyofoptimalmethodsfornonlinearequationswithchemicalengineeringapplications
AT ishakhashim efficacyofoptimalmethodsfornonlinearequationswithchemicalengineeringapplications
_version_ 1725230858937303040

Similar Items