On improved three-step schemes with high efficiency index and their dynamics

A new family of four-step fifteenth-order root-finding methods with high efficiency index

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

A Three-Point Iterative Method for Solving Nonlinear Equations with High Efficiency Index

In this paper, we proposed a three-point iterative method for finding the simple roots of non- linear equations via mid-point and interpolation approach. The method requires one evaluation of the derivative and three(3) functions evaluation with efficiency index of 81/4 ≈ 1.682. Numerical results reported here, between the proposed method with some other existing methods shows that our method i...

A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX

It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...

a new family of four-step fifteenth-order root-finding methods with high efficiency index

‎in this paper a new family of fifteenth-order methods with high efficiency index is presented‎. this family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎in order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

Step-Index PMMA Fibers and Their Applications