**Meet the editor**

Dr. Terry E. Moschandreou is a professor in Applied Mathematics at the University of Western Ontario in the School of Mathematical and Statistical Sciences where he has taught for several years. He received his PhD degree in Applied Mathematics from the University of Western Ontario in 1996. The greater part of his professional life was spent at the University of Western

Ontario and Fanshawe College in London, Ontario, Canada. For a short period, he worked at the National Technical University of Athens, Greece. Dr. Moschandreou is the author of several research articles in blood flow and oxygen transport in the microcirculation, general fluid dynamics and theory of differential equations. Also, he has contributed in the field of finite element modelling of the upper airways in sleep apnea and surgical brain deformation modelling. More recently, he has been working with the partial differential equations of multiphase flow and level set methods as used in fluid dynamics.

Contents

**Preface VII**

**Section 1 Theory of Differential Equations 1**

**Differential Equations 3**

**Arbitrary Order 35** Kamal Shah and Yongjin Li

Hamid Ibrahim Ouglu

**Poincare Circle 65**

Cheon Seoung Ryoo

Chapter 6 **Reproducing Kernel Functions 99**

**Landau Equation 117** Tarek Aboelenen

Ali Akgül and Esra Karatas Akgül

**Section 2 Applications of Differential Equations 115**

Chapter 2 **Existence Theory of Differential Equations of**

Chapter 4 **Phase Portraits of Cubic Dynamic Systems in a**

Irina Andreeva and Alexey Andreev

Chapter 1 **Fixed Point Theory Approach to Existence of Solutions with**

Chapter 3 **An Extension of Massera's Theorem for N-Dimensional Stochastic Differential Equations 57**

Chapter 5 **Differential Equations Arising from the 3-Variable Hermite Polynomials and Computation of Their Zeros 81**

Chapter 7 **Local Discontinuous Galerkin Method for Nonlinear Ginzburg-**

Piyachat Borisut, Konrawut Khammahawong and Poom Kumam

Boudref Mohamed Ahmed, Berboucha Ahmed and Osmanov
