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Torkashvand, Vali, Kazemi, Manochehr, Azimi, Masoud. (1403). Efficient family of three-step with-memory methods and their dynamics. سامانه مدیریت نشریات علمی, 12(3), 599-609. doi: 10.22034/cmde.2023.55761.2324
Vali Torkashvand; Manochehr Kazemi; Masoud Azimi. "Efficient family of three-step with-memory methods and their dynamics". سامانه مدیریت نشریات علمی, 12, 3, 1403, 599-609. doi: 10.22034/cmde.2023.55761.2324
Torkashvand, Vali, Kazemi, Manochehr, Azimi, Masoud. (1403). 'Efficient family of three-step with-memory methods and their dynamics', سامانه مدیریت نشریات علمی, 12(3), pp. 599-609. doi: 10.22034/cmde.2023.55761.2324
Torkashvand, Vali, Kazemi, Manochehr, Azimi, Masoud. Efficient family of three-step with-memory methods and their dynamics. سامانه مدیریت نشریات علمی, 1403; 12(3): 599-609. doi: 10.22034/cmde.2023.55761.2324

Efficient family of three-step with-memory methods and their dynamics

Computational Methods for Differential Equations
مقاله 13، دوره 12، شماره 3، مهر 2024، صفحه 599-609    اصل مقاله (719.92 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55761.2324
نویسندگان
Vali Torkashvand* 1، 2؛ Manochehr Kazemi3؛ Masoud Azimi2
1Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Shahr-e-Qods, Iran.
2Department of Mathematics , Farhangian University , Tehran, Iran.
3Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.
چکیده
In this work, we have proposed a general manner to extend some two-parametric with-memory methods to obtain simple roots of nonlinear equations. Novel improved methods are two-step without memory and have two self-accelerator parameters that do not have additional evaluation. The methods have been compared with the nearest competitions in various numerical examples. Anyway, the theoretical order of convergence is verified. The basins of attraction of the suggested methods are presented and corresponded to explain their interpretation.
کلیدواژه‌ها
With-memory method؛ Basin of attraction؛ Accelerator parameter؛ $R$-order convergence؛ Nonlinear equations
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