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

Subject Areas : International Journal of Mathematical Modelling & Computations

Taher Lotfi ¹ , Paria Assari ²

1 - Isalmic Azad University- Hamedan Branch Nonlinear Systems of EquationsInterval Analysis Absolute Value EquationsGeneralized inversesMoore_penrose InversesReproducing kernel methods
2 - Isalmic Azad University- Hamedan Branch

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

Keywords: Nonlinear equation, With memory method, R-order of convergence, self-accelerating parameter,

Abstract :

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 step applying only information from the current and the previous iteration, defining a with memory class. Although these improvements are achieved without any additional function evaluations, the $ R $-order of convergence are boosted from 4 to 5.24 and 6, respectively, and it is demonstrated that the proposed with memory classes provide a very high computational efficiency. Numerical examples are put forward and the performances are compared with the basic two-step without memory methods.