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## Meet the editor

Bruno Carpentieri obtained a laurea degree in Applied Mathematics in 1997 from Bari University, Italy. He obtained a Ph.D. in Computer Science from the Institut National Polytechnique de Toulouse (INPT), France. After some post-doctoral experiences, Dr. Carpentieri served as an assistant professor at the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, the Netherlands, and as a

reader in Applied Mathematics at Nottingham Trent University, United Kingdom. Since May 2017, he has been an associate professor of Applied Mathematics at the Faculty of Computer Science, Free University of Bozen-Bolzano, Italy. His research interests include applied mathematics, numerical linear algebra, and high-performance computing. Dr. Carpentieri has served on several scientific advisory boards in computational mathematics. He is an editorial board member of the *Journal of Applied Mathematics*, an editorial committee member of *Mathematical Reviews* (American Mathematical Society) and a reviewer for about thirty scientific journals in numerical analysis. He has co-authored fifty publications in peer-reviewed scientific journals.

Contents

**Preface XIII**

**Chapter 1 1**

**Chapter 2 25**

**Chapter 3 43**

**Chapter 4 65**

**Chapter 5 85**

**Chapter 6 97**

**Chapter 7 119**

Using the Boundary Element Method to Simulate Visco-Elastic

Asymptotic Behavior by Krasnoselskii Fixed Point Theorem for Nonlinear Neutral Differential Equations with Variable Delays

Spectral Properties of a Non-Self-Adjoint Differential Operator

Deformed Sine-Gordon Models, Solitons and Anomalous Charges *by Harold Blas, Hector F. Callisaya, João P.R. Campos, Bibiano M. Cerna* 

Continuous One Step Linear Multi-Step Hybrid Block Method for the Solution of First Order Linear and Nonlinear Initial Value

Existence and Asymptotic Behaviors of Nonoscillatory Solutions

Global Existence of Solutions to a Class of Reaction–Diffusion

*by Kamoh Nathaniel, Kumleng Geoffrey and Sunday Joshua*

with Block-Triangular Operator Coefficients

Problem of Ordinary Differential Equations

of Third Order Time Scale Systems

Deformations of Rough Fractures

*by Hao Kang*

*by Benhadri Mimia*

*by Aleksandr Kholkin*

*and Carlos Reyes*

*by Özkan Öztürk*

Systems on *<sup>n</sup> by Salah Badraoui*

## Contents



**III**

**Chapter 19 307**

**Chapter 20 319**

**Chapter 21 339**

Boundary Element Method for the Mixed BBM-KdV Equation Compared

On the Generalized Simplest Equations: Toward the Solution of Nonlinear

*by Gunawan Nugroho, Purwadi Agus Darwito, Ruri Agung Wahyuono* 

Thermodynamic Stability Conditions as an Eigenvalues Fundamental

*by Mostafa Abounouh, Hassan Al-Moatassime, Sabah Kaouri* 

Differential Equations with Variable Coefficients

to Non Standard Boundary Conditions

*and Youssef Ouakrim*

*and Murry Raditya*

*by Francisco Nogueira Lima*

Problem


*by Francisco Nogueira Lima*

**II**

**Chapter 8 135**

**Chapter 9 145**

**Chapter 10 163**

**Chapter 11 181**

**Chapter 12 195**

**Chapter 13 217**

**Chapter 14 227**

**Chapter 15 241**

**Chapter 16 263**

**Chapter 17 277**

**Chapter 18 295**

The Fourier Transform Method for Second-Order Integro-Dynamic

Effect of Additive Perturbations on the Solution of Reflected Backward

On Some Important Ordinary Differential Equations of Dynamic

Multiple Solutions for Some Classes Integro-Dynamic Equations

Solution of Nonlinear Partial Differential Equations by Mixture Adomian Decomposition Method and Sumudu Transform

Positive Periodic Solutions for First-Order Difference Equations

Peculiarities of the Fundamental Solution of Parabolic Systems

Bio-Thermomechanical Problems of Anisotropic Soft Tissues

Solving Second-Order Differential Equations by Decomposition

Boundary Element Modeling and Simulation Algorithm for Fractional

The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded

Gradient Optimal Control of the Bilinear Reaction–Diffusion Equation

*by Mesliza Mohamed, Gafurjan Ibragimov and Seripah Awang Kechil*

Equations on Time Scales *by Svetlin G. Georgiev*

*by Jasmina Ðorđević*

*by Anastasios Tsoularis*

Economics

on Time Scales *by Svetlin G. Georgiev*

with Impulses

with a Negative Genus

*by Fritz Schwarz*

Domains

*by Vladyslav Antonovich Litovchenko*

*by Mohamed Abdelsabour Fahmy*

*by Tair Gadjiev and Konul Suleymanova*

*by El Hassan Zerrik and Abderrahman Ait Aadi*

Stochastic Differential Equations

*by Tarig M. Elzaki and Shams E. Ahmed*

Preface

Nonlinear differential equations are ubiquitous in computational science and in engineering modeling, for example, in fluid dynamics, finance, quantum mechanics, material science, medical applications, and biology, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theoretical analysis of such systems (investigation of the existence and stability of analytical solutions, study of bifurcation and of chaotic dynamics, etc.) and the development and use of sophisticated computational methods that can guide and support the theoretical findings by practical computer simulations.

This book is not a standard textbook on the solution of nonlinear differential equations. There is already an extensive treatment on the subject on the market. The purpose of this volume is to discuss some significant developments of the last years on the definition of new theories, models, computer algorithms, and applications relating to the solution of nonlinear differential equations in various scientific areas. It collects research papers written by leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically

The book includes contributions that contain both theory-oriented chapters and more applied ones. As such, it will lead to a deeper understanding and appreciation of the research produced in this fascinating field. Researchers, engineers, and graduate students in both pure and applied mathematics will benefit from reading

We express appreciation to IntechOpen for professional support and Author Service Manager Dr. Kristina Kardum Cvitan for her tireless help in the preparation of this

**Bruno Carpentieri**

Bolzano, Italy

Faculty of Computer Science, Free University of Bozen-Bolzano,

important area of mathematics and modern science.

the papers collected in this volume.

book.
