Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming

This research aimed to investigate the most efficient iterative method in solving scalarnonlinear equations. There are three iterative methods that are used to solve the nonlinearscalar equations that are Bisection, Secant and Newton Raphsons methods. Thesethree iterative methods have different orde...

Full description

Saved in:

Bibliographic Details
Main Author:	Aboamemah, Ahmed Hadi Mohammed
Format:	thesis
Language:	eng
Published:	2019
Subjects:	QA Mathematics
Online Access:	https://ir.upsi.edu.my/detailsg.php?det=6475
Tags:	Add Tag No Tags, Be the first to tag this record!

id	oai:ir.upsi.edu.my:6475
record_format	uketd_dc
institution	Universiti Pendidikan Sultan Idris
collection	UPSI Digital Repository
language	eng
topic	QA Mathematics
spellingShingle	QA Mathematics Aboamemah, Ahmed Hadi Mohammed Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming
description	This research aimed to investigate the most efficient iterative method in solving scalarnonlinear equations. There are three iterative methods that are used to solve the nonlinearscalar equations that are Bisection, Secant and Newton Raphsons methods. Thesethree iterative methods have different order of convergence. Bisection method is linearlyconvergence while Secant method is super linear and Newton-Raphson methodhas quadratic convergence. It is well known that the method that has a higher orderof convergence, will perform much faster than others. Seven nonlinear scalar equationsare considered based on the combinations of two or three functions and are solvedby the Bisection, Secant and Newton-Raphson methods using Scilab programming language.The tolerance used is 1010 and the performances of these methods are based onnumber of function evaluation, number of iterations, and computational or CPU time.Based on the numerical results of the seven nonlinear equations, it is observed thatNewton-Raphson method is still the most efficient method but not for all the equations.Bisection method has fixed performances on all the nonlinear equations however, themethod failed to converge for the imaginary root. On the other hand, the performanceof Secant method is almost similar to Newton-Raphson method except for the nonlinearEquations (4.4), and (4.5) on the interval [1.3,2] and [0,1] respectively. In conclusion,Newton-Raphson method remains the best but not for all nonlinear equations sincethere are realistic circumstances that makes Newton-Raphson converges either sloweror identical to Secant method. It is also proven that Secant method can perform fasterthan Newton-Raphson method depending on the form of the curve functions that correspondsto the approximate values. As implications, more than three combinations ofthe functions can be investigated and also the research can be extended to system ofnonlinear equations.
format	thesis
qualification_name
qualification_level	Master's degree
author	Aboamemah, Ahmed Hadi Mohammed
author_facet	Aboamemah, Ahmed Hadi Mohammed
author_sort	Aboamemah, Ahmed Hadi Mohammed
title	Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming
title_short	Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming
title_full	Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming
title_fullStr	Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming
title_full_unstemmed	Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming
title_sort	numerical study on some iterative methods for solving nonlinear equations by using scilab programming
granting_institution	Universiti Pendidikan Sultan Idris
granting_department	Fakulti Sains dan Matematik
publishDate	2019
url	https://ir.upsi.edu.my/detailsg.php?det=6475
_version_	1747833267016433664
spelling	oai:ir.upsi.edu.my:64752021-11-25 Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming 2019 Aboamemah, Ahmed Hadi Mohammed QA Mathematics This research aimed to investigate the most efficient iterative method in solving scalarnonlinear equations. There are three iterative methods that are used to solve the nonlinearscalar equations that are Bisection, Secant and Newton Raphsons methods. Thesethree iterative methods have different order of convergence. Bisection method is linearlyconvergence while Secant method is super linear and Newton-Raphson methodhas quadratic convergence. It is well known that the method that has a higher orderof convergence, will perform much faster than others. Seven nonlinear scalar equationsare considered based on the combinations of two or three functions and are solvedby the Bisection, Secant and Newton-Raphson methods using Scilab programming language.The tolerance used is 1010 and the performances of these methods are based onnumber of function evaluation, number of iterations, and computational or CPU time.Based on the numerical results of the seven nonlinear equations, it is observed thatNewton-Raphson method is still the most efficient method but not for all the equations.Bisection method has fixed performances on all the nonlinear equations however, themethod failed to converge for the imaginary root. On the other hand, the performanceof Secant method is almost similar to Newton-Raphson method except for the nonlinearEquations (4.4), and (4.5) on the interval [1.3,2] and [0,1] respectively. In conclusion,Newton-Raphson method remains the best but not for all nonlinear equations sincethere are realistic circumstances that makes Newton-Raphson converges either sloweror identical to Secant method. It is also proven that Secant method can perform fasterthan Newton-Raphson method depending on the form of the curve functions that correspondsto the approximate values. As implications, more than three combinations ofthe functions can be investigated and also the research can be extended to system ofnonlinear equations. 2019 thesis https://ir.upsi.edu.my/detailsg.php?det=6475 https://ir.upsi.edu.my/detailsg.php?det=6475 text eng closedAccess Masters Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik Adhikari, I. (2017). Interval and speed of convergence on iterative methods. HimalayanPhysics, 6:112114.Akram, S. and Ul Ann, Q. (2015). Newton raphson method. International Journal of Scienti?c &Engineering Research, 6(7):17481752.Al-Baali, M., Spedicato, E., and Maggioni, F. (2014). Broydens quasi-newton methods for anonlinear system of equations and unconstrained optimization: a review and open problems.Optimization Methods and Software, 29(5):937954.Burden, R. L., Faires, J. D., and Burden, A. (2014). Numerical analysis. Brooks/Cole, USA.Candela, V. and Peris, R. (2015). The rate of multiplicity of the roots of nonlinear equa- tionsand its application to iterative methods. Applied Mathematics and Computation, 264:417430.Chhabra, C. (2014). Improvements in the bisection method of ?nding roots of an equa- tion. AdvanceComputing Conference (IACC), 2014 IEEE International, 2014:1116.Dez, P. (2003). A note on the convergence of the secant method for simple and multiple roots.Applied Mathematics Letters, 16(8):12111215.Ehiwario, J. C. and Aghamie, S. O. (2014). Comparative study of bisection, newton- raphson andsecant methods of root-?nding problems. IOSR Journal of Engineering (IOSRJEN), 4(04):22788719.Hasan, A. (2016). Numerical study of some iterative methods for solving nonlinear equations.International Journal of Engineering Science Invention, 5(2):0110.Hasan, A. and Ahmad, N. (2015). Comparative study of a new iterative method with that of newtonsmethod for solving algebraic and transcendental equations. 4(3):32 37.Henrici, P. (1964). Elements of Numerical Analysis. Wiley, Switzerland.Intep, S. (2018). A review of bracketing methods for ?nding zeros of nonlinear func-tions. Applied Mathematical Sciences, 12(3):137146.Jain, M. K. (2003). Numerical methods for scienti?c and engineering computation.New Age International.Kumar, R. and Vipan (2015). Comparative analysis of convergence of various numerical methods.Journal of Computer and Mathematical Sciences, 6(6):290297.McClarren, R. G. (2018a). Chapter 12 - Closed Root Finding Methods, pages 215228.Academic Press, USA.McClarren, R. G. (2018b). Chapter 13 - Open Root Finding Methods, pages 229249.Academic Press, USA.Nijmeijer, M. J. P. (2014). A method to accelerate the convergence of the secant algo- rithm.Advances in Numerical Analysis, 2014:114.Papakonstantinou, J. M. and Tapia, R. A. (2013). Origin and evolution of the secant method in onedimension. The American Mathematical Monthly, 120(6):500517.Polyak, B. T. (2007). Newtons method and its use in optimization. European Journal of OperationalResearch, 181(3):10861096.Ramos, H. and Vigo-Aguiar, J. (2015). The application of newtons method in vector form for solvingnonlinear scalar equations where the classical newton method fails. Journal of Computational andApplied Mathematics, 275:228237.Salleh, Z., Yusop, M. Y. M., and Ismail, S. B. (2012). Basic of numerical computa- tional usingscilab programming. Proceedings of the 2nd International Conference on Mathematical Applicationsin Engineering (ICMAE2012), 2012:18.Shanker, G. R. (2006). Numerical analysis. New Age International, New Delhi.Solanki, C., Thapliyal, P., and Tomar, K. (2014). Role of bisection method. Interna-tional Journal of Computer Applications Technology and Research, 3(9):533535.Srivastava, R. B. and Srivastava, S. (2011). Numerical rate of convergence of bisection method.Journal of Chemical, Biological and Physical Sciences (JCBPS), 2(1):451 461.Vianello, M.and Zanovello, R. (1992). On the superlinear convergence of the secantmethod. The American mathematical monthly, 99(8):758761.Walter, E. (2014). Numerical methods and optimization. Springer, United States. Zarowski, C. J.(2004). An introduction to numerical analysis for electrical and com-puter engineers. John Wiley & Sons, New York.

Numerical study on some iterative methods for solving nonlinear equations by using Scilab programming

Similar Items