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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2015 by IJMTT Journal
Volume-19 Number-2
Year of Publication : 2015
Authors : Abdulaziz G. Ahmad
  10.14445/22315373/IJMTT-V19P516

MLA

Abdulaziz G. Ahmad"Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems", International Journal of Mathematics Trends and Technology (IJMTT). V19(2):121-129 March 2015. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
This paper presents two numerical techniques of root- nding 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- nding is also been discussed. The software pack- age, MATLAB 7.6 was used to nd 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].

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