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Fractional Newton–Raphson Method Accelerated with Aitken’s Method [PDF]
Axioms, 2021 In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is ...
A. Torres-Hernandez +3 more
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Modeling Of Active Bending By The Method Newton-Raphson And The Modified Newton-Raphson
Civil and Environmental EngineeringThe paper deals with the modelling and analysis of a single layer timber gridshell produced by active bending. Two geometrically nonlinear calculation methods, the Newton-Raphson method and the Modified Newton-Raphson method, are compared for the ...
Herda Roman +2 more
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Fractional Newton-Raphson Method
Applied Mathematics and Sciences An International Journal (MathSJ), 2021 The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we
Torres Hernandez, Anthony +1 more
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The development of Newton’s method by enhancing the starting point
International Journal of Trends in Mathematics Education Research, 2023 In general, nonlinear problems cannot be solved analytically. A special theory or method is needed to simplify calculations. Many problems that are too complex, an exact solution is needed to support numerical solution.
Ismi Ratin Nabiyah +2 more
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Cauchy: Jurnal Matematika Murni dan Aplikasi, 2021 This study discusses the analysis of the modification of Newton-Secant method and solving nonlinear equations having a multiplicity of by using a modified Newton-Secant method.
Juhari Juhari
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Newton–Raphson based scalar speed control and optimization of IM
Automatika, 2021 In this study, Newton–Raphson Based (NRB) scalar speed control (SSC) is recommended to control the speed of Induction Motors (IM). As is known, the Newton–Raphson method, which is often used in numerical analysis, is one of the methods that provide a ...
Özcan Otkun
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Adaptation of the Newton-Raphson and Potra-Pták methods for the solution of nonlinear systems
Semina: Ciências Exatas e Tecnológicas, 2021 In this paper we adapt the Newton-Raphson and Potra-Pták algorithms by combining them with the modified Newton-Raphson method by inserting a condition.
Luiz Antonio Farani de Souza +2 more
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On Fractional Newton-Type Method for Nonlinear Problems
Journal of Mathematics, 2022 The current manuscript is concerned with the development of the Newton–Raphson method, playing a significant role in mathematics and various other disciplines such as optimization, by using fractional derivatives and fractional Taylor series expansion ...
Mine Aylin Bayrak +2 more
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IET Generation, Transmission & Distribution, 2022 The energy flow calculation of the integrated electric power and natural gas system (IEGS) is generally tackled by the classical Newton–Raphson (NR) method with second‐order convergence.
J.H. Zheng +4 more
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Mechanical Engineering Journal, 2021 Quasi-Newton-based nonlinear finite element methods were extensively studied in the 1970s and 1980s. However, they have almost disappeared due to their poorer convergence performance than the Newton-Raphson method.
Yasunori YUSA +2 more
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