NDLI: Fractional Newton–Raphson Method Accelerated with Aitken's Method

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Fractional Newton–Raphson Method Accelerated with Aitken's Method

Content Provider	MDPI
Author	U. Iturrarán-Viveros, Torres-Hernandez, A. Brambila-Paz, F. Caballero-Cruz, R.
Copyright Year	2021
Description	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 different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.
Starting Page	47
e-ISSN	20751680
DOI	10.3390/axioms10020047
Journal	Axioms
Issue Number	2
Volume Number	10
Language	English
Publisher	MDPI
Publisher Date	2021-03-31
Access Restriction	Open
Subject Keyword	Axioms Mathematical Physics Newton–raphson Method Fractional Calculus Fractional Derivative Aitken's Method
Content Type	Text
Resource Type	Article

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