APPLICATION OF NUMERICAL ANALYSIS TO ALGEBRAIC AND TRANSCENDENTAL EQUATIONS

ABSTRACT

In this paper we introduce, numerical study of some iterative methods for solving non linear equations. Many iterative methods for solving algebraic and transcendental equations are presented by the different formulae. Using bisection method, false position method, secant method and the Newton’s iterative method and their results are compared. The bisection, Regular Falsi, Newton-Raphson and secant method were applied to a single variable function over the interval [0,1]. Numerical rate of convergence of root has been found in each calculation. It was observed that the Bisection method converges at the 10th iteration while Newton and Secant methods converge to the exact root of 0.7390 with error level at the 5th iteration respectively. It was also observed that the Newton   method required less number of iteration in comparison to that of secant method. However, when we compare performance, we must compare both cost and speed of convergence. It was then concluded that of the four methods considered, Secant method is the most effective and more efficient than others.