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

A. Torres-Hernandez^*,a, F. Brambila-Paz^†,b, P. M. Rodrigo^‡,c,d, and E. De-la-Vega^§,c

a. Department of Physics, Faculty of Science – UNAM, Mexico
b. Department of Mathematics, Faculty of Science – UNAM, Mexico
c. Faculty of Engineering, Universidad Panamericana – Aguascalientes, Mexico
d. Centre for Advanced Studies in Energy and Environment (CEAEMA), University of Jaen, Spain.

Abstract: A nonlinear algebraic equation system of 5 variables is numerically solved, which 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.

Keywords: Iteration Function, Order of Convergence, Fractional Derivative, Parallel Chord Method, Hybrid Solar Receiver.

Pages: 285 – 299 | Full PDF Paper