جستجوی مقالات مرتبط با کلیدواژه « adaptive methods » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه « adaptive methods » در نشریات گروه « علوم پایه »-
In this work, we have constructed the with memory two-step method with four convergence degrees by entering the maximum self-accelerator parameter(three parameters). Then, using Newton’s interpolation, a with-memory method with a convergence order of 7.53 is constructed. Using the information of all the steps, we will improve the convergence order by one hundred percent, and we will introduce our method with convergence order 8. Numerical examples demonstrate the exceptional convergence speed of the proposed method and confirm theoretical results. Finally, we have presented the dynamics of the adaptive method and other without-memory methods for complex polynomials of degrees two, three, and four. The basins of attraction of existing with-memory methods are present and compared to illustrate their performance.Keywords: Nonlinear equations, Basin of attraction, Adaptive methods, R-order convergence, Self accelerating parameter}
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The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as high efficiency indices as possible.
Keywords: Nonlinear equations, Iterative methods, Steffensen-like method, Methods with memory, Adaptive methods}
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