Reduction of a nonlinear system and its numerical solution using a fractional iterative method

Abstract

A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the efficiencies of a hybrid solar receiver, which in simple terms is the combination of a photovoltaic system with a thermoelectric system. In addition, a way to reduce the previous system to a nonlinear system of only 2 variables is presented. Naturally, reducing algebraic equation systems of dimension N to systems of smaller dimensions has the main advantage of reducing the number of variables involved in a problem, but the analytical expressions of the systems become more complicated. However, to minimize this disadvantage, an iterative method that does not explicitly depend on the analytical complexity of the system to be solved is used. A fractional iterative method, valid for one and several variables, that uses the properties of fractional calculus, in particular the fact that the fractional derivatives of constants are not always zero, to find solutions of nonlinear systems is presented.

arXiv admin note: substantial text overlap with arXiv:2006.14963, arXiv:1804.08445; text overlap with arXiv:2004.10860

References in corpus (2)

• The maximum theoretical performance of unconcentrated solar photovoltaic and thermoelectric generator systems
• An approximation to zeros of the Riemann zeta function using fractional calculus

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