Acceleration of the order of convergence of a family of fractional fixed point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers

TL;DR

This paper introduces a novel approach to accelerate the convergence of fractional fixed point methods, enabling efficient solutions to nonlinear algebraic systems in hybrid solar receiver models.

Contribution

It defines, classifies, and accelerates the convergence order of an uncountable family of fractional fixed point methods, with practical application to solar receiver systems.

Findings

Accelerated convergence in fractional fixed point methods.

Successful solution of nonlinear algebraic systems for solar receivers.

Enhanced computational efficiency in fractional iterative methods.

Abstract

This paper presents a way to define, classify and accelerate the order of convergence of an uncountable family of fractional fixed point methods, which may be useful to continue expanding the applications of fractional operators. The proposed method to accelerate convergence is used in a fractional iterative method, and with the obtained method are solved simultaneously two nonlinear algebraic systems that depend on time-dependent parameters, and that allow obtaining the temperatures and efficiencies of a hybrid solar receiver. Finally, two uncountable families of fractional fixed point methods are presented, in which the proposed method to accelerate convergence can be implemented.