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A COMPARATIVE STUDY OF NUMERICAL METHODS IN SOLVING ROOTS OF NONLINEAR EQUATIONS

Abstract

We solved nonlinear equations such as cubic equation x^3 − 2x − 5 = 0 and transcendental equations like sin x = x/2 (or equivalently, sin x − x/2 = 0) with three different classical numerical methods These methods were (a) Bisection method, (b) Newton-Raphson method, and (c) Secant method. We implemented these methods manually to solve the nonlinear equations mentioned above and compared their performance in terms of speed (iterations numbers), accuracy (proximity to true root), and reliability (convergence behavior and sensitivity to initial conditions). Our observation showed that the Newton-Raphson method was the fasted among all three methods in consideration.

Acknowledgements

CUR, Albany State University, Albany GA

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