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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 19 | Number 2 | Year 2015 | Article Id. IJMTT-V19P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V19P516

Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems


Abdulaziz G. Ahmad
Abstract

This paper presents two numerical techniques of root-finding problems of a non- linear equations with the assumption that a solution exists, the rate of convergence of Bisection method and Newton-Rhapson method of root-finding is also been discussed. The software pack- age, MATLAB 7.6 was used to and the root of the function, f(x) = cosx-x*exp(x) on a close interval [0; 1] using the Bisection method and Newton's method the result was compared. It was observed that the Bisection method converges at the 14th iteration while Newton methods converge to the exact root of 0:5718 with error 0.0000 at the 2nd iteration respectively. It was then concluded that of the two methods considered, Newton's method is the most effective scheme. This is in line with the result in our Ref.[9].

Keywords
Convergence, Roots, Algorithm, MATLAB Code, Iterations, Bisection method, Newton-Rhapson method and function
References

[1] Burden, R.L., Faires, J.D. 2011 Numerical Analysis 9th Edition, Brook/Cole, a part of Cengage Learning.
[2] Joe D. Ho man, 1992 Numerical Method for Engineers and Scientist, McGraw-Hill, Inc Newyork.
[3] Rudra Pratap, 2013 Getting Started With MATLAB: A Quick Introduction For Science and Engineers, Oxford University Press.
[4] Butcher J.C, 2003 Numerical Method for ordinary di erential equation, John Wiley and Sons Ltd UK.
[5] Kendalle E. Atkinson, 2004 An Introduction To Numerical Analysis, John Wiley and Sons Ltd UK.
[6] Radhey S. Gupta, 2009 Element of Numerical Analysis, Macmillan India Ltd.
[7] Chadha, N.M, 2014 Lecture Note On MATLAB, Sharda University.
[8] Cleve B. Moler, Numerical Computing With MATLAB, PHI Leraning, Rimjhim house Delhi, 2013.
[9] Noreen, Jamil, A Comparison of Iterative Methods for the Solution of Non-Linear Systems of equations,Int. J. Emerg. Sci., 3(2), 119-130, June 2013

Citation :

Abdulaziz G. Ahmad, "Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 19, no. 2, pp. 121-129, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V19P516

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