Modified Newton's method using harmonic mean for solving nonlinear equations

Jayakumarand Kalyanasundaram
2013 IOSR Journal of Mathematics  
Different modifications in the Newton's method with cubic convergence have become popular iterative methods to find the roots of non-linear equations. In this paper, a modified Newton's method for solving a single nonlinear equation is proposed. This method uses harmonic mean while using Simpson's integration rule, thus replacing ′ in the classical Newton's method. The convergence of the proposed method is found to be order three. Numerical examples are provided to compare e the efficiency of
more » ... the efficiency of the method with few other cubic convergent methods.
doi:10.9790/5728-0749397 fatcat:f2kzry6ubvfrvlhetn5wpv74na