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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1972.
|
| Colección: | Mathematics in science and engineering ;
v. 18-II. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 082 | 0 | 4 | |a 515/.355 |2 23 |
| 100 | 1 | |a Ames, William F. | |
| 245 | 1 | 0 | |a Nonlinear partial differential equations in engineering. |n Volume II / |c W.F. Ames. |
| 260 | |a New York : |b Academic Press, |c 1972. | ||
| 300 | |a 1 online resource (xi, 305 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering ; |v v. 18-II | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 1.11 Parametrization and the Legendre Transformation1.12 B�acklund Transformations; 1.13 An Example B�acklund 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Differential equations, Nonlinear. | |
| 650 | 0 | |a Differential equations, Partial. | |
| 650 | 6 | |a �Equations diff�erentielles non lin�eaires. |0 (CaQQLa)201-0041487 | |
| 650 | 6 | |a �Equations aux d�eriv�ees partielles. |0 (CaQQLa)201-0012495 | |
| 650 | 7 | |a Differential equations, Nonlinear |2 fast |0 (OCoLC)fst00893474 | |
| 650 | 7 | |a Differential equations, Partial |2 fast |0 (OCoLC)fst00893484 | |
| 776 | 0 | 8 | |i Print version: |a Ames, William F. |t Nonlinear partial differential equations in engineering. |d New York : Academic Press, 1972 |w (DLC) 65022767 |
| 830 | 0 | |a Mathematics in science and engineering ; |v v. 18-II. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780120567553 |z Texto completo |