Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems

This study has been discussed a trapezoidal iterated method for estimating a single root of nonlinear problems, which arises in many scientific and engineering fields. The proposed iterative method has second order of convergence, and derived from trapezoidal rule. Several numerical examples to illu...

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Main Authors: Umair Khalid Qureshi, Zubair Ahmed Kalhoro, Asif Ali Shaikh, Abdul Rehman Nangraj
Format: Article
Language:English
Published: University of Sindh 2018-04-01
Series:University of Sindh Journal of Information and Communication Technology
Subjects:
Online Access:http://sujo.usindh.edu.pk/index.php/USJICT/article/view/4231/2840
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author Umair Khalid Qureshi
Zubair Ahmed Kalhoro
Asif Ali Shaikh
Abdul Rehman Nangraj
author_facet Umair Khalid Qureshi
Zubair Ahmed Kalhoro
Asif Ali Shaikh
Abdul Rehman Nangraj
author_sort Umair Khalid Qureshi
collection DOAJ
description This study has been discussed a trapezoidal iterated method for estimating a single root of nonlinear problems, which arises in many scientific and engineering fields. The proposed iterative method has second order of convergence, and derived from trapezoidal rule. Several numerical examples to illustrate the efficiency of proposed method by Comparison with the famous second order convergence Newton Raphson Method. C++ and EXCELL are used to analyze the results and graphical representations of proposed method. Henceforth, it has been observed from the outcomes and assessment of trapezoidal iterative method with the Newton Raphson Method that the trapezoidal second order method is performance healthier than existing method.
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spelling doaj.art-93dcb66e65ba4fc9b2946f814ed8d4b62022-12-21T16:53:55ZengUniversity of SindhUniversity of Sindh Journal of Information and Communication Technology2521-55822523-12352018-04-0122111114Trapezoidal Second Order Convergence Method for Solving Nonlinear ProblemsUmair Khalid Qureshi0Zubair Ahmed Kalhoro1Asif Ali Shaikh2Abdul Rehman Nangraj3Department of Basic Science & Related Studies, Mehran University of Engineering and technology, PakistanInstitute Mathematics and Computer Science, University of Sindh Jamshoro, PakistanDepartment of Basic Science & Related Studies, Mehran University of Engineering and technology, PakistanInstitute Mathematics and Computer Science, University of Sindh Jamshoro, PakistanThis study has been discussed a trapezoidal iterated method for estimating a single root of nonlinear problems, which arises in many scientific and engineering fields. The proposed iterative method has second order of convergence, and derived from trapezoidal rule. Several numerical examples to illustrate the efficiency of proposed method by Comparison with the famous second order convergence Newton Raphson Method. C++ and EXCELL are used to analyze the results and graphical representations of proposed method. Henceforth, it has been observed from the outcomes and assessment of trapezoidal iterative method with the Newton Raphson Method that the trapezoidal second order method is performance healthier than existing method.http://sujo.usindh.edu.pk/index.php/USJICT/article/view/4231/2840non-linear problemstrapezoidal ruleorder of convergenceabsolute percentage erroraccuracy.
spellingShingle Umair Khalid Qureshi
Zubair Ahmed Kalhoro
Asif Ali Shaikh
Abdul Rehman Nangraj
Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems
University of Sindh Journal of Information and Communication Technology
non-linear problems
trapezoidal rule
order of convergence
absolute percentage error
accuracy.
title Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems
title_full Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems
title_fullStr Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems
title_full_unstemmed Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems
title_short Trapezoidal Second Order Convergence Method for Solving Nonlinear Problems
title_sort trapezoidal second order convergence method for solving nonlinear problems
topic non-linear problems
trapezoidal rule
order of convergence
absolute percentage error
accuracy.
url http://sujo.usindh.edu.pk/index.php/USJICT/article/view/4231/2840
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AT zubairahmedkalhoro trapezoidalsecondorderconvergencemethodforsolvingnonlinearproblems
AT asifalishaikh trapezoidalsecondorderconvergencemethodforsolvingnonlinearproblems
AT abdulrehmannangraj trapezoidalsecondorderconvergencemethodforsolvingnonlinearproblems