Two new three and four parametric with memory methods for solving nonlinear equations
Publish Year: 1394
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJIM-7-3_008
تاریخ نمایه سازی: 27 دی 1402
Abstract:
In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. ۵۷ (۲۰۱۳) ۱۹۵۰-۱۹۵۶], we develop two new iterative with memory methods for solving a nonlinear equation. The first has two steps with three self-accelerating parameters, and the second has three steps with four self-accelerating parameters. These parameters are calculated using information from the current and previous iteration so that the presented methods may be regarded as the with memory methods. The self-accelerating parameters are computed applying Newton's interpolatory polynomials. Moreover, they use three and four functional evaluations per iteration and corresponding R-orders of convergence are increased from ۴ ad ۸ to ۷.۵۳ and ۱۵.۵۱, respectively. It means that, without any new function calculations, we can improve convergence order by ۹۳\% and ۹۶\%. We provide rigorous theories along with some numerical test problems to confirm theoretical results and high computational efficiency.
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