دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات43
تعداد شماره‌ها1,253
تعداد مقالات15,411
تعداد مشاهده مقاله51,245,944
تعداد دریافت فایل اصل مقاله14,254,182
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
مراجع
  • [1] S. Amat, S. Busquier, and S. Plaza, Dynamics of the King and Jarratt iterations, Aequationes mathematicae, 69 (3) (2005), 212–223.
  • [2] W. Bi, Q. Wu, and H. Ren, A new family of eighth-order iterative methods for solving nonlinear equations, Applied Mathematics and Computation, 214 (1) (2009) 236–245.
  • [3] G. Candelario, A. Cordero, J.R. Torregrosa, and M.P. Vassileva, An optimal and low computational cost fractional Newton-type method for solving nonlinear equations, Applied Mathematics Letters, 124 (2022), 107650.
  • [4] B. Campos, A. Cordero, J.R. Torregrosa, and P. Vindel, Dynamical analysis of an iterative method with memory on a family of third-degree polynomials, AIMS Mathematics, 7(4) 6445–6466.
  • [5] C. Chun, B. Neta, J. Kozdon, and M. Scott, Choosing weight functions in iterative methods for simple roots, Applied Mathematics and Computation, 227 (2014), 788–800.
  • [6] F. Chicharro, A. Cordero, J. M. Guti´errez, and J.R. Torregrosa, Complex dynamics of derivative-free methods for nonlinear equations, Applied Mathematics and Computation, 219 (12) (2013), 7023–7035.
  • [7] B. Campos, A. Cordero Barbero, J. R, Torregrosa S´anchez, and P. Vindel Canas, Stability of King’s family of iterative methods with memory, Journal of Computational and Applied Mathematics, 318 (2017) 504–514.
  • [8] A. Cordero Barbero, M. Fardi, M. Ghasemi, and J. R. Torregrosa, Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior, Calcolo, 51 (1) (2014) 17–30
  • [9] A. Cordero, H. Ramos, and J. R. Torregrosa, Some variants of Halley’s method with memory and their applications for solving several chemical problems, Journal of Mathematical Chemistry, 58 (2020) 751–774.
  • [10] H. T. Kung and J. F. Traub, Optimal order of one-point and multi-point iteration, J. ACM, 21 (4) (1974) 643–651.
  •  [11] S. Kumar, D. Kumar, J. R. Sharma, and I. K. Argyros, An efficient class of fourth-order derivative-free method for multiple-roots, International Journal of Nonlinear Sciences and Numerical Simulation, 24 (1) (2023) 265–275.
  • [12] T. Lotfi, S. Sharifi, M. Salimi and S. Siegmund, A new class of three-point methods with optimal convergence order eight and its dynamics, Numerical Algorithms, 68 (2) (2015) 261–288.
  • [13] M. Moccari and T. Lotfi, On a two-step optimal Steffensen-type method: Relaxed local and semi-local convergence analysis and dynamical stability, Journal of Mathematical Analysis and Applications, 468 (1) (2018) 240–269.
  • [14] M. Moccari, T. Lotfi, and V. Torkashvand, On Stability of a Two-Step Method for a Fourth-degree Family by Computer Designs along with Applications, International Journal of Nonlinear Analysis and Applications (IJNAA), 14 (4) (2023) 261–282.
  • [15] M. Mohamadi Zadeh, T. Lotfi, and M. Amirfakhrian, Developing two efficient adaptive Newton-type methods with memory, Mathematical Methods in the Applied Sciences, 42 (17) (2019) 5687–5695.
  • [16] B. Neta, A sixth order family of methods for nonlinear equations, International Journal of Computer Mathematics, 7 (1979) 157–161.
  • [17] A.M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, 1960.
  • [18] M.S. Petkovi´c, B. Neta, L.D. Petkovi´c, and J. Dˇzuni´c, Multipoint Methods for Solving Nonlinear Equations, Elsevier, Amsterdam, 2013.
  • [19] J. R. Sharma and H. Arora, Some novel optimal eighth order derivative-free root solvers and their basins of attraction, Applied Mathematics and Computation, 284 (2016) 149–161.
  • [20] J. R. Sharma and H. Arora, A new family of optimal eighth order methods with dynamics for nonlinear equations, Applied Mathematics and Computation, 273 (2016) 924–933.
  • [21] A. R. Soheili and F. Soleymani, Iterative methods for nonlinear systems associated with finite difference approach in stochastic differential equations, Numerical Algorithms, 71 (1) (2016) 89–102.
  • [22] A. R. Soheili, M. Amini, and F. Soleymani, A family of Chaplygin-type solvers for Itoˆ stochastic differential equations, Applied Mathematics and Computation, 340 (2019) 296–304.
  • [23] F. Soleymani, On a bi-parametric class of optimal eighth-order derivative-free methods, International Journal of Pure and Applied Mathematics, 72 (1) (2011) 27–37.
  • [24] F. Soleymani, Several iterative methods with memory using self-accelerators, Journal of the Egyptian Mathematical Society, 21 (2) (2013) 133–141.
  • [25] J. Steffensen, Remarks on iteration, Scandinavian Actuarial Journal, 1933(1), 64–72.
  • [26] J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
  • [27] V. Torkashvand, T. Lotfi, and M. A. Fariborzi Araghi, A new family of adaptive methods with memory for solving nonlinear equations, Mathatical Sciences, 13 (1) (2019) 1–20.
  • [28] V. Torkashvand and M. Kazemi, On an Efficient Family with Memory with High Order of Convergence for Solving Nonlinear Equations, International Journal of Industrial Mathematics, 12 (2) (2020), 209–224.
  • [29] V. Torkashvand, A two-step method adaptive with memory with eighth-order for solving nonlinear equations and its dynamic, Computational Methods for Differential Equations, 50 (1) (2022) 1007–1026.
  • [30] V. Torkashvand and M. A. Fariborzi Araghi, Construction of Iterative Adaptive Methods with Memory with 100% Improvement of Convergence Order, Journal of Mathematical Extension, 15 (3) (16) (2021) 1–32.
  • [31] Vali Torkashvand, Transforming Ostrowski’s method into a derivative-free method and its dynamics, Computational Mathematics and Computer Modeling with Applications, 2 (1) (2023) 1–10.
  • [32] M. Z. Ullah, V, Torkashvand, S. Shateyi, and M. Asma, Using matrix eigenvalues to construct an iterative method with the highest possible efficiency index two, Mathematics, 10 (1370) 2022 1–15.
  • [33] H. Veiseh, T. Lotfi, and T. Allahviranloo, A study on the local convergence and dynamics of the two-step and derivative-free Kung-Traub’s method, Computational and Applied Mathematics, 37 (3) (2018) 2428–2444.
  • [34] X. Wang, A new accelerating technique applied to a variant of Cordero-Torregrosa method, Journal of Computational and Applied Mathematics, 330 (2018) 695–709.
آمار
تعداد مشاهده مقاله: 72
تعداد دریافت فایل اصل مقاله: 141


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب