A Closer Look of Nonlinear Reaction-diffusion Equations

✍ Scribed by L. Rajendran, R. Swaminathan

• Publisher: Nova Science Pub Inc
• Tongue: English
• Leaves: 209
• Category: Library

✦ Synopsis

"By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area. Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science. This book contains seven chapters and practical applications to the problems of the real world"--

✦ Table of Contents

Contents
Preface
Acknowledgments
Chapter 1
Fundamentals of Nonlinear Reaction-Diffusion Equations
1.1. Nonlinear Reaction-Diffusion System
1.2. Application of Nonlinear Reaction-Diffusion System
1.2.1. Biological Sciences
1.2.2. Chemical Sciences
1.2.3. Medical Sciences
1.2.4. Physical Sciences
1.2.5. Engineering Sciences
1.3. Some Important Nonlinear Reaction-Diffusion Equations
1.4. Various Analytical Methods for Finding the Solution of Nonlinear Equations
References
Chapter 2
Mathematical Preliminaries and Various Methods of Solving Nonlinear Differential Equations
2.1. Overview
2.2. Various Methods of Solving Nonlinear Differential Equations
2.3. Analytical Methods with Basic Explanation and Examples
2.3.1. Homotopy Perturbation Method (HPM)
2.3.1.1. Basic Idea of Homotopy Perturbation Method
2.3.1.2. Example: Polymer-Modified Ultramicroelectrodes
2.3.2. Homotopy Analysis Method (HAM)
2.3.2.1. Basic Idea of Homotopy Analysis Method
2.3.2.2. Example: Steady-State Biofilters
2.3.3. Adomian Decomposition Method
2.3.3.1. Basic Concepts of the Adomian Decomposition Method (ADM)
2.3.3.2. Example: Substrate Inhibition Kinetics in an Immobilized Enzyme
2.3.4. Variational Iteration Method (VIM)
2.3.4.1. Basic Concepts in the Variational Iteration Method
2.3.4.2. Example: Electrochemical Immobilization of Enzymes
2.3.5. Exp-Function Method
2.3.5.1. Basic Concept of Exp-Function Method
2.3.5.2. Example: Mass Transport in Heterogeneous Catalysis
2.3.6. Hyperbolic Function Method
2.3.6.1. Basic Concept of Hyperbolic Function Method
2.3.6.2. Example: Glucose Oxidase Enzyme System
2.3.7. Variational Fractal Theory
2.3.7.1. Example: Troesch’s Problem
2.3.8. Taylor Series and Padé Approximation Method
2.3.8.1. Taylor Series
2.3.8.2. Padé Approximation
2.3.8.3. Example: Electroactive Polymers
2.3.8.4. Parameter-Expanding Methods
2.3.9. Parameterized Perturbation Method
References
Chapter 3
Steady and Non-Steady State Reaction-Diffusion Equations in Plane Sheet
3.1. Introduction
3.2. Concentration of Carbon Dioxide (CO2), and Phenyl Glycidyl Ether Solution (PGE) Using Taylor’s Series and Padé Approximation
3.3. Analytical Solution One Dimensional Nonlinear Parabolic Partial Differential Equation in Chemical Sciences
References
Chapter 4
Steady and Non-Steady State Nonlinear Reaction-Diffusion in a Cylinder
4.1. Introduction
4.2. Concentration of Methanol Using HPM Method
4.3. Analytical Solution of Various Nonlinear Boundary Value Problems in Cylindrical Coordinates
References
Chapter 5
Steady and Non-Steady Nonlinear Reaction-Diffusion in a Sphere
5.1. Introduction
5.2. Concentration of Spherical Catalytic Particle in Immobilized Enzyme System
5.3. Analytical Solution of Various Nonlinear Boundary Value Problems in Spherical Coordinates
References
Chapter 6
Nonlinear Convection-Diffusion Problems
6.1. Introduction
6.2. Electrochemical Convection Diffusion Phenomena at the Rotating Disk Electrode
6.3. Nonlinear Convection Diffusion Equations and Corresponding Analytical Solutions in Various Fields of Chemical Sciences
References
Chapter 7
Numerical Methods
7.1. Introduction
7.2. Advantage of Numerical Methods
7.3. Various Numerical Methods
7.4. New Computational Methods Using Software
7.5. Analytical and Numerical (Matlab) Solutions of the Coupled Reaction and Diffusion Equations within Polymer-Modified Ultramicroelectrodes
7.6. Numerical Simulation
References
About the Authors
Index
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