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

International Journal of Mathematical Modelling & Computations

مقاله 7، دوره 4، 3 (SUMMER)، فروردین 2014، صفحه 277-288   

نویسندگان

Taher Lotfi¹؛ Paria Assari²

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

²Isalmic Azad University- Hamedan Branch

چکیده

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.

کلیدواژه‌ها

Nonlinear equation؛ With memory method؛ R-order of convergence؛ self-accelerating parameter