Nonlinear Ordinary Differential Equations in Transport Processes
Published on 14. May 2014
281 pages
978-0-08-095550-6 (ISBN)
Description
Nonlinear Ordinary Differential Equations in Transport Processes
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095550-6 (9780080955506)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
William F. Ames
Nonlinear Ordinary Differential Equations in Transport Processes
Book
06/1968
Academic Press
€75.52
Article exhausted; check different version
Content
- 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
