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Research Article

Generalized multistep Steffensen iterative method. Solving the model of a photomultiplier device

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Pages 1839-1859 | Received 24 Jan 2022, Accepted 18 May 2023, Published online: 02 Jun 2023
 

Abstract

It is well known that the Steffensen-type methods approximate the derivative appearing in Newton's scheme by means of the first-order divided difference operator. The generalized multistep Steffensen iterative method consists of composing the method with itself m times. Specifically, the divided difference is held constant for every m steps before it is updated. In this work, we introduce a modification to this method, in order to accelerate the convergence order. In the proposed, scheme we compute the divided differences in first and second step and use the divided difference from the second step in the following m−1 steps. We perform an exhaustive study of the computational efficiency of this scheme and also introduce memory to this method to speed up convergence without performing new functional evaluations. Finally, some numerical examples are studied to verify the usefulness of these algorithms.

AMS 2020 SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially supported by Ministerio de Economía y Competitividad [grant number PGC2018-095896-B-C22].

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