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

Abstract

The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; it is necessary to mention that the solution of the aforementioned system is relatively difficult to obtain through iterative methods since the system is apparently 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 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.