UID:
almahu_9947366122702882
Umfang:
1 online resource (527 p.)
ISBN:
1-282-28988-8
,
9786612289880
,
0-08-095524-X
Serie:
Mathematics in science and engineering ; 18
Inhalt:
Nonlinear Partial Differential Equations in Engineering: v. 1
Anmerkung:
Description based upon print version of record.
,
Front Cover; Nonliner Partial Differential Equations in Engineering, Volume 18; Copyright Page; Contents; Preface; CHAPTER 1. The Origin of Nonlinear Differential Equations; 1.0 Introduction; 1.1 What is Nonlinearity?; 1.2 Equations from Diffusion Theory; 1.3 Equations from Fluid Mechanics; 1.4 Equations from Solid Mechanics; 1.5 Miscellaneous Examples; 1.6 Selected References; References; CHAPTER 2. Transformation and General Solutions; 2.0 Introduction; 2.1 Transformations on Dependent Variables; 2.2 Transformations on Independent Variables; 2.3 Mixed Transformations
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2.4 The Unknown Function Approach2.5 General Solutions; 2.6 General Solutions of First-Order Equations; 2.7 General Solutions of Second-Order Equations; 2.8 Table of General Solutions; References; CHAPTER 3. Exact Methods of Solution; 3.0 Introduction; 3.1 The Quasi-Linear System; 3.2 An Example of the Quasi-Linear Theory; 3.3 The Poisson-Euler-Darboux Equation; 3.4 Remarks on the PED Equation; 3.5 One-Dimensional Anisentropic Flows; 3.6 An Alternate Approach to Anisentropic Flow; 3.7 General Solution for Anisentropic Flow; 3.8 Vibration of a Nonlinear String
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3.9 Other Examples of the Quasi-Linear Theory3.10 Direct Separation of Variables; 3.11 Other Solutions Obtained by Ad Hoc Assumptions; References; CHAPTER 4. Further Analytic Method; 4.0 Introduction; 4.1 An Ad Hoc Solution from Magneto-Gas Dynamics; 4.2 The Utility of Lagrangian Coordinates; 4.3 Similarity Variables; 4.4 Similarity via One-Parameter Groups; 4.5 Extensions of the Similarity Procedure; 4.6 Similarity via Separation of Variables; 4.7 Similarity and Conservation Laws; 4.8 General Comments on Transformation Groups; 4.9 Similarity Applied to Moving Boundary Problems
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4.10 Similarity Considerations in Three Dimensions4.11 General Discussion of Similarity; 4.12 Integral Equation Methods; 4.13 The Hdograph; 4.14 Simple Examples of Hodograph Application; 4.15 The Hodograph in More Complicated Problems; 4.16 Utilization of the General Solutions of Chapter 2; 4.17 Similar Solutions in Heat and Mass Transfer; 4.18 Similarity Integrals in Compressible Gases; 4.19 Some Disjoint Remarks; References; CHAPTER 5. Approximate Methods; 5.0 Introduction; 5.1 Perturbation Concepts; 5.2 Regular Perturbations in Vibration Theory; 5.3 Perturbation and Plasma Oscillations
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5.4 Perturbation in Elasticity5.5 Other Applications; 5.6 Perturbation about Exact Solutions; 5.7 The Singular Perturbation Problem; 5.8 Singular Perturbations in Viscous Flow; 5.9 The "Inner-Outer'' Expansion (a Motivation); 5.10 The Inner and Outer Expansions; 5.11 Examples; 5.12 Higher Approximations for Flow past a Sphere; 5.13 Asymptotic Approximations; 5.14 Asymptotic Solutions in Diffusion with Reaction; 5.15 Weighted Residual Methods: General Discussion; 5.16 Examples of the Use of Weighted Residual Methods; 5.17 Comments on the Methods of Weighted Residuals
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5.18 Mathematical Problems of Approximate Methods
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English
Weitere Ausg.:
ISBN 0-12-056756-3
Sprache:
Englisch
