Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems. Given an irreducible non-negative power series system with m equations, let ρ be the radius of convergence of the solution power series and let τ be the values of the solu...

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

In this paper, a simple algorithm based on a two-diode circuit model of the solar cell is proposed for calculating different parameters of PV panels. The input parameters required for this algorithm are available from datasheets of the standard PV modules. The values of series and parallel resistances, as well as the recombination factor of Diode 2, are estimated through an iterative solution p...

Absrtact: In this study, a numerical algorithm for solving a generalization of a functional differential equation known as the pantograph equation is presented. Firstly, the proposed algorithm produces an approximate polynomial solution as a power series for the problem. Then, we transform the obtained power series into Padé series form to obtain an approximate polynomial of an arbitrary order ...

We present a new method for the numerical solution of the Hamilton Jacobi Bellman PDE that arises in an infinite time optimal control problem. The method can be of higher order to reduce ”the curse of dimensionality”. It proceeds in two stages. First the HJB PDE is solved in a neighborhod of the origin using the power series method of Al’brecht. From a boundary point of this neighborhood, an ex...