Nonlinear partial differential equations in engineering, Volume II
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrang...
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| Format: | eBook |
| Language: | English |
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New York
Academic Press
1972, 1972
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| Series: | Mathematics in science and engineering
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| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- 2.14 Transformation of Boundary-Value Problems into Initial-Value Problems- Simultaneous EquationsReferences; Chapter 3. Approximate Methods; 3.0 Introduction; 3.1 Weighted Residual Methods (WRM); 3.2 Novel Applications of WRM in Fluid Mechanics; 3.3 WRM in Transport Phenomena-Some Recent Literature; 3.4 WRM in Dynamics and Solid Mechanics; 3.5 Comments on WRM Theory; 3.6 Maximum Principles-Ordinary Differential Equations; 3.7 Maximum Principles-Partial Differential Equations; 3.8 Quasi Linearization; 3.9 Regular Perturbation and Irregular Domains; 3.10 Classical Regular Perturbation
- 2.4 Incorporation of the Auxiliary Conditions2.5 Determination of Absolute Invariants; 2.6 Example of Deductive Similarity Method; 2.7 Similarity Formalism with Multiparameter Groups; 2.8 Infinitesimal Transformations; 2.9 Classical Determination of Infinitesimal Transformations; 2.10 Nonclassical Determination of Infinitesimal Transformations; 2.11 The Nonclassical Method and Simultaneous Equations; 2.12 Some Similarity Literature; 2.13 Transformation of Boundary-Value Problems into Initial-Value Problems-Single Equations
- Includes bibliographical references and indexes
- 1.11 Parametrization and the Legendre Transformation1.12 Bäcklund Transformations; 1.13 An Example Bäcklund Transformation; 1.14 First Integrals; 1.1 5 Development of First Integrals; 1.16 Lagrange Series Solutions; 1.17 Breakdown Theory of Jeffrey-Lax; 1.18 Application of the Jeffrey-Lax Method; 1.19 Dynamics of Moving Threadline; 1.20 Ballooning Vibration of a Moving Threadline; References; Chapter 2. Applications of Modern Algebra; 2.0 Introduction; 2.1 The Similarity Method of Morgan; 2.2 Application of the Morgan Method; 2.3 Determination of Groups by Finite Transformations
- 3.11 The Perturbation Method of Keller et al3.12 Singular Perturbation; 3.13 Lighthill's Method of Strained Coordinates; 3.14 Miscellaneous Asymptotic Procedures; References; Chapter 4. Numerical Methods; 4.0 Introduction; A. Finite Elements; 4.1 Introduction to Finite Elements; 4.2 Formulation of Finite Element Characteristics; 4.3 Theoretical Comments on Displacement Functions; 4.4 Additional Elements in Two and Three Dimensions; 4.5 Finite Elements and Field Problems; 4.6 Finite Elements and Nonlinear Problems; B. Numerical Solutions in Fluid Mechanics; 4.7 Preliminary Remarks
- Front Cover; Nonlinear Partial Differential Equations in Engineering; Copyright Page; Contents; Preface; Contents of Volume I; Chapter 1. Analytic Techniques and Solutions; 1.0 Introduction; 1.1 Nonlinear Superposition Principles; 1.2 Generation of Nonlinear Equations with Built-in Solutions; 1.3 Employing the Wrong Equation to Find the Right Solution; 1.4 Application of the Quasi-Linear Theory; 1.5 Earnshaw's Procedure; 1.6 Traveling-Wave Solutions; 1.7 Arbitrary Functions; 1.8 Equation Splitting; 1.9 Inversion of Dependent and Independent Variables; 1.10 Contact Transformations