Journal of Al-Qadisiyah for Computer Science and Mathematics

In this paper we investigate new definitions called Partial Modular (P.M) and Convex Partial Modular (C.P.M) which are generalized of the definitions Modular and Convex Modular respectively . We can satisfy some results and properties of a partial modular (P.M) and we deduced some result in convex partial modular (C.P.M) . Finally we get a new study of relation between (P.M) and modular.

In the work, we study the general properties of modified of the
Bogdanov map in the form Fa,m,k .

In the present work, new efficient iterative algorithm is presented for solving Lane-Emden
equation with initial conditions. The solution is considered as a linear combination of VietaFibonacci polynomials with unknown coefficients. First, the Vieta-Fibonacci polynomials are
presented with some new important properties. A new exact formula for finding operation
matrix of derivative for the Vieta-Fibonacci polynomials is constructed. Using such new
properties the original Lane-Emden equation is transformed to the solution of algebraic
equation with small-unknown coefficients. The obtained solution is in the form of a power
series with easily computable coefficients. Comparison with some known exact and
approximate solutions shows that the proposed solution is highly accurate.

In this paper, we find the conditions for the sequence of characteristic zero in the case of the
skew-shape (9,7,3)/(1,0). We also study this sequence as a diagram and prove that this sequence is
complex using mapping Cone and other concepts.

The aim of this work is to find the complex of characteristic zero (c.c.z.) in the case of skewpartition (6, 6, 3) / (1, 1, 0) as a diaǥram by utilizing the conceᶈts poweг of ᶈlaҫe polariẕaŧion
and Caᶈęlli ideᶇtities.

In this work, we present numerical method in order to solve non-linear equation of solar cell
based on single diode model using two suitable approximations; Illinois Algorithm and Classic
Chord techniques. Algorithms have discussed the tolerances of the values. It is founded that
the new proposed method has the lesser number of evaluations than the other ones.
Numerical examples are presented in order to test the efficiency, accuracy and the
performance of this method. Numerical calculations observe that the proposed method is
compatible with the famous existing methods and in this case gives the better results. The
results obtained explain that the new suggested technique is more easy, accurate to use and
efficient than other numerical methods are introduced.

In the present work, two iterative techniques have been displayed in order to solve non-linear
equation. These two techniques are free from second derivative and per evaluation; they
require five and six iterations with a first derivative of the function. Analysis of the PV model
has been studied in term of function evaluations appears that the proposed technique is
superior. It is practical interest is investigated by some numerical examples.

A general class of three point iterative algorithms for solving nonlinear equations based on
single diode model of a PV cell is constructed in the present work. Three steps iterative
methods for solving nonlinear equation of solar cell, Illinois Algorithm and Two-Point
Bracketing algorithm are presented and analyzed. In addition; the absolute error values for all
the algorithms have been discussed and compared. The new proposed method has the lesser
number of iterations than the other ones has been founded. Numerical examples are
contained to test and investigate the performance, accuracy and efficiency of these methods

In the present work, we exhibit a third order family of a new iteration method Dekker's and
Classic Chord methods for solving nonlinear equations of single diode solar cell model. These
methods have free from computation of second order derivatives of the functions and per
iteration, one estimation of the function; while just two evaluations involving it is first
derivative. Analysis of this family of these numerical methods investigates that it is iterative
solution is convergence. Some numerical examples are introduced to show the accuracy,
efficiency and good performance of the proposed method.