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

Abdulaziz G. Ahmad

doi:https://doi.org/10.14445/22315373/IJMTT-V19P516

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

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

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

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