**
1. **
**Solving Nonlinear Equations Using Two-Step
Optimal Methods**
Full text (PDF)

**M.A. Hafiz, M. S. M. Bahgat**

**
Pages: 1-11**

**
Abstract:
** Finding
iterative methods for solving nonlinear equations is an important area
of research in numerical analysis at it has interesting applications in
several branches of pure and applied science can be studied in the
general framework of the nonlinear equations f(x)=0. Due to their
importance, several numerical methods have been suggested and analyzed
under certain condition. These numerical methods have been constructed
using different techniques such as Taylor series, homotopy perturbation
method and its variant forms, quadrature formula, variational iteration
method, and decomposition method ( see [1-9]). In this study we describe
new iterative free from second derivative to find a simple root r of a
nonlinear equation. In the implementation of the method of Noor et al.
[10], one has to evaluate the second derivative of the function, which
is a serious drawback of these methods. To overcome these drawbacks, we
modify the predictor-corrector Halley method by replacing the second
derivatives of the function by its suitable finite difference scheme.

**2. **
**A Dynamical Analysis of an Autocatalytic Model****
Full
text (PDF)**

**Lakshmi Burra, Uma Maheswari**

**
Pages: 12-22**

**
Abstract:
**In this paper we study an autocatalytic reaction and we derive
the differential equations arising from this reaction. We analyze these
equations using phase-space analysis. We next use Center Manifold theory
to derive a stable Center Manifold for this system. Since this system is
a polynomial differential system, we study the orbits of the system
which go or come from infinity using the
Poincaré compactification.
Interestingly these equations would also represent a population model.
All these concepts are illustrated graphically.

**3. **
**Chaos in the Planar Two-Body Coulomb Problem with a Uniform
Magnetic Field**
Full text (PDF)

**Vladimir Zhdankins, J. C. Sprott****
**
**
**

**
Pages: 23-33**

**
Abstract:
** The dynamics of the
classical two-body Coulomb problem in a uniform magnetic field are
explored numerically in order to determine when chaos can occur. The
analysis is restricted to the configuration of planar particles with an
orthogonal magnetic field, for which there is a four-dimensional phase
space. Parameters of mass and charge are chosen to represent physically
motivated systems. To check for chaos, the largest Lyapunov exponent and
Poincaré section are determined for each case. We find chaotic solutions
when particles have equal signs of charge. We find cases with opposite
signs of charge to be numerically unstable, but a Poincaré section
shows that chaos occurs in at least one case.

4**.
**
**On a Conjecture of Trichotomy and Bifurcation in a Third Order
Rational Difference Equation****
**
Full text (PDF)

** ****Xianyi****
****Li, Cheng Wang**

**
Pages: 34-44**

**
Abstract:
** In this
paper it is first investigated for a conjecture of trichotomy of period
two for a third order rational difference equation, and then the
bifurcation of this equation is further considered. The results obtained
partially verify a conjecture in the known literature.

**
5.
Book Review: Lozi Mappings: Theory and
Applications, by Zeroualia Elhadj, CRC Press, 2013
**Full text (PDF)

**René Lozi****
**

**
Pages: 45-48**

**
Abstract:
** When,
more than two years ago, Prof. Zeroualia Elhadj informed me of his
willing to write a book on what is known as *Lozi map* since the
Misiurewicz's communication in the congress organized by the New York
Academy of Science, 17-21 December 1979, I warned the task was not
straightforward because hundreds of articles were published on this
topic in thirty years. These papers were scattered in various fields of
research, not only in mathematics (dynamical systems), but in physics,
computer science, electronics, chemistry, control science and
engineering, etc..

**
**