Graphical and Numerical Study of a Newly Developed Root-Finding Algorithm and Its Engineering Applications

The primary objective of this paper is to develop a new method for root-finding by combining forward and finite-difference techniques in order provide an efficient, derivative-free algorithm with lower processing cost per iteration. This will be accomplished techniques. We also detail the convergence criterion that was devised approach, we show recommended quintic-order convergent. addressed few engineering issues illustrate validity application developed algorithm. quantitative results justified constructed algorithm’s robust performance comparison other methods can found literature. For graphical analysis, make use newly discovered plot some novel polynomiographs are attractive eye, then evaluate these plots relation previously established strategies. graphic analysis demonstrates created has better larger area than comparable do.