IOSR Journal of Engineering (IOSRJEN) Comparative Study of Bisection, Newton-Raphson and Secant Methods of Root-Finding Problems (original) (raw)
The study is aimed at comparing the rate of performance, viz-aviz, the rate of convergence of Bisection method, Newton-Raphson method and the Secant method of root-finding. The software, mathematica 9.0 was used to find the root of the function, f(x)=x-cosx on a close interval [0,1] using the Bisection method, the Newton's method and the Secant method and the result compared. It was observed that the Bisection method converges at the 52 second iteration while Newton and Secant methods converge to the exact root of 0.739085 with error 0.000000 at the 8 th and 6 th iteration respectively. It was then concluded that of the three methods considered, Secant method is the most effective scheme. This is in line with the result in our Ref. .
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Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems
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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 package , MATLAB 7.6 was used to find 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 14 th iteration while Newton methods converge to the exact root of 0.5718 with error 0.0000 at the 2 nd 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].
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