Fractional pseudo-Newton method and its use in the solution of a nonlinear system that allows the construction of a hybrid solar receiver

A. Torres-Hernandez, F. Brambila-Paz, E. De-la-Vega

The following document presents a possible solution for a nonlinear system that models the construction of a hybrid solar receiver, it is necessary to mention that the solution of the aforementioned system is relatively difficult to obtain by iterative methods since the system is unstable. To find this possible solution is used a novel numerical method valid for one and several variables, which using the fractional derivative, allows us to find solutions for some nonlinear systems in the complex space using real initial conditions, this method is also valid for linear systems. The method described above receives the name of the fractional pseudo-Newton method, which has an order of convergence (at least) linear, but it is easy to implement and it is not necessary to invert some matrix for solving nonlinear systems and linear systems. In the nonlinear system mentioned, which is obtained by studying the possibility of building a hybrid solar receiver, its stability is briefly analyzed, as well as where a possible solution is found and finally it is solved using the fractional pseudo-Newton method.

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