Nonlinear ordinary differential equations in transport processes / William F. Ames.

Format:

Book

Author/Creator:

Ames, William F.

Series:

Mathematics in science and engineering ; v. 42.

Mathematics in science and engineering ; 42

Language:

English

Subjects (All):

Differential equations, Nonlinear.

Transport theory.

Physical Description:

1 online resource (281 p.)

Place of Publication:

New York : Academic Press, 1968.

Language Note:

English

Summary:

Nonlinear Ordinary Differential Equations in Transport Processes

Contents:

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 Equations2.1 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 Curves2.18 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 MethodsIntroduction; 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 ApproximationReferences; 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

Notes:

Description based upon print version of record.

Includes bibliographies and index.

ISBN:

1-282-28987-X

9786612289873

0-08-095550-9

OCLC:

316566892