A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX
نویسندگان
چکیده مقاله:
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.
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عنوان ژورنال
دوره 4 شماره 3 (SUMMER)
صفحات 277- 288
تاریخ انتشار 2014-03-21
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