Nonlinear Ordinary Differential Equations in Transport Processes

Name: Nonlinear Ordinary Differential Equations in Transport Processes
Brand: Academic Press
Price: 76.95 EUR
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Roger Ames(Autor*in)

Roger Ames(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

281 Seiten

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978-0-08-095550-6 (ISBN)

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Front Cover
Nonlinear Ordinary Differential Equations in Transport Processes
Copyright Page
CONTENTS
Preface
Chapter 1. The Origin of Nonlinear Equations
Introduction
1.1 What Is Nonlinearity?
1.2 Other Departures from Linear Theory
1.3 Literature
1.4 Examples in Kinetics
1.5 Heat Transfer and Chemical Reaction
1.6 Equations from ad-hoc Methods for Partial Differential Equations
1.7 Equations from Similarity Solutions
1.8 Population Growth and Other Problems in Biological Sciences
1.9 Radiation Heat Transfer
References
Chapter 2. Exact Methods of Solution
Introduction
First Order Equations
2.1 The Integrating Factor
2.2 Homogeneous Equation
2.3 General First Order Equations
2.4 Solution by Transformation
2.5 Further Solution by Differentiation
Second Order Equations
2.6 The Simplest Equations
2.7 Elliptic Integrals
2.8 Elliptic Functions
2.9 Equations with Form Homogeneity
2.10 Raising the Order
2.11 A Transformation of Euler
2.12 Equations Equivalent to Linear Equations
2.13 The Group Concept
2.14 Infinitesimal Transformations
2.15 Representation of Infinitesimal Transformations
2.16 Invariant Functions
2.17 Invariant Points, Curves, and Families of Curves
2.18 The Extended Group
2.19 Integration of First Order Equations
2.20 Equations Invariant under Specific Groups
2.21 Extension to Second Order Equations
References
Chapter 3. Examples from Transport Phenomena
Introduction
3.1 Matrices and Chemical Reactions
3.2 Kinetics and the Z Transform
3.3 Kinetics and Heat Transfer
3.4 Equations of Lane-Emden Type
3.5 Some Similarity Equations from Fluid Mechanics
3.6 Conversion of Boundary Value to Initial Value Problems
3.7 Nonlinear Equations from Diffusion
References
Chapter 4. Approximate Methods
Introduction
4.1 Some Mathematical Properties
4.2 Series Expansion
4.3 Methods of Iteration
4.4 Operational Iterative Methods
4.5 Application of Iterative Methods
4.6 Regular Peturbation
4.7 Shohat's Expansion
4.8 Singular Perturbation
4.9 The Method of Strained Coordinates
4.10 Comparison of the Two Preceding Methods
4.11 Weighted Residual Methods-General Discussion
4.12 Example of Weighted Residuals
4.13 Comments on the Method of Weighted Residuals
4.14 Quasilinearization
4.15 Applications of Quasilinearization
4.16 Other Methods of Approximation
References
Chapter 5. Numerical Methods
Introduction
5.1 Finite Differences
5.2 One Step Methods
5.3 Runge-Kutta Methods
5.4 Simultaneous Equations
5.5 Multi-Step Methods
5.6 Choice of Predictor-Corrector Method
5.7 Boundary Value Problems
5.8 Components of an Electronic Analog Computer
5.9 Analog Circuits for Simple Operations
5.10 Scaling Procedures and Initial Conditions
5.11 Examples
References
Appendix. Similarity Variables by Transformation Groups
Text
References
Author Index
Subject Index

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